
655 F.3d 1323 (2011)
Lyman F. BUSH Individually and as Personal Representative of the Estate of Beverly J. Bush, Plaintiffs-Appellants,
v.
UNITED STATES, Defendant-Appellee.
Tommy J. Shelton, Plaintiff-Appellant,
v.
United States, Defendant-Appellee.
Nos. 2009-5008, 2009-5009.
United States Court of Appeals, Federal Circuit.
August 24, 2011.
*1324 Thomas E. Redding, Redding & Associates, P.C., of Houston, TX, argued for all plaintiffs-appellants. With him on the brief were Sallie W. Gladney and Teresa J. Womack.
Andrew M. Weiner, Attorney, Appellate Section, Tax Division, United States Department of Justice, of Washington, DC, argued for defendant-appellee. With him on the brief were John A. Dicicco, Acting Deputy Assistant Attorney General, and Michael J. Haungs, Attorney.
Before RADER, Chief Judge, NEWMAN, LOURIE, BRYSON, GAJARSA,[*] LINN, DYK, PROST, MOORE, O'MALLEY, and REYNA, Circuit Judges, on rehearing en banc.
Opinion for the court filed by Circuit Judge PROST, in which Chief Judge RADER and Circuit Judges LOURIE, BRYSON, GAJARSA, MOORE and O'MALLEY, join. Dissenting opinion filed by Circuit Judge DYK, in which Circuit Judges NEWMAN, LINN, and REYNA join.
PROST, Circuit Judge.
This tax case concerns the procedures to be followed when the Internal Revenue Service ("IRS" or "government") conducts a partnership proceeding under the Tax Equity and Fiscal Responsibility Act of 1982 ("TEFRA"). I.R.C. §§ 6221-6233. The plaintiffs are individual taxpayers and limited partners in partnerships that were the subject of such proceedings. The plaintiffs opted out of the partnership proceedings via settlement. In doing so, they stipulated to certain matters concerning their participation in the partnerships. Based on those stipulations, the IRS assessed recomputed taxes against the plaintiffs without first issuing notices of deficiency (which would have triggered an opportunity for plaintiffs to challenge the recomputation in the United States Tax Court before assessment). Plaintiffs paid the assessed taxes and subsequently filed suit on grounds that the lack of deficiency notices rendered the assessments invalid. The United States Court of Federal Claims ruled for the government, holding that the IRS had no obligation to issue notices of deficiency in such circumstances. Bush v. United States, 78 Fed. Cl. 76 (2007); Shelton v. United States, Nos. 02-1042, 04-1595, 2007 U.S. Claims LEXIS 311 (Aug. 17, 2007). We agree, and therefore affirm.

I
Before turning to the facts, we undertake a brief review of TEFRA and its effect on the IRS's auditing of partnerships. When an individual taxpayer prepares his yearly tax return, he self-computes his tax for income he has earned, then transmits the appropriate payment. Matters become more complicated where income generated by partnerships is involved. The partnership generates income, but as an entity is not itself taxable. Instead, the individual partners of a partnership shoulder the burden of taxation on income that the partnership generates.
In order for the IRS to properly audit the individual returns of the partners, it must have data about the partnership's income as a whole. For that reason, partnerships are required to file yearly returns, even though they do not pay tax on income. The IRS can then audit the partnership return against the returns of the partners and have a more complete picture of the income generated, which leads to a more accurate assessment of tax liability all around.
TEFRA comes into play when the IRS reviews a partnership return and disputes *1325 some aspect of it. One of the Act's purposes was to streamline the tax procedures for partnerships. Rather than undertake an arduous series of partner-by-partner audits, as had previously been required, TEFRA allows for a single, unified audit to determine the treatment of "partnership items" for all the partners. See I.R.C. §§ 6221-6233; H.R. Conf. Rep. No. 97-760, at 599-600 (1982); see also Callaway v. Comm'r, 231 F.3d 106, 107-08 (2d Cir. 2000); Keener v. United States, 76 Fed.Cl. 455, 457-58 (2007), aff'd, 551 F.3d 1358 (Fed.Cir.2009). These are items whose treatment affects the entire partnership, and so analyzing them at the partnership level makes more sense than doing so partner-by-partner. See I.R.C. § 6231(a)(3) (defining "partnership item").
Under TEFRA, the IRS performs its audit of the partnership return and then transmits a notice of any required adjustments to each of the partners, as well as to the partnership's Tax Matters Partner. If the partnership wishes to dispute the outcome of the audit, the Tax Matters Partner may file a petition in court. See id. § 6226(a)(1)-(3). All partners are treated as parties and have a right to participate in the judicial proceeding, and if they wish can settle independently with the IRS. See id. § 6224(c).
This case involves such settlements, and questions about the proper procedure for the IRS when it endeavors to collect taxes it believes are owed pursuant to the settlement.

II
We turn, then, to the facts. The two appeals before us present the same issues and nearly identical stories. The first, case number XXXX-XXXX, concerns taxpayer Lyman Bush and his late wife Beverly Bush. In the early 1980s, Mr. Bush was a limited partner in two partnerships, respectively named Lone Wolf McQuade and Cinema '84. As part of their obligations under the Tax Code, the partnerships filed tax returns. As individual taxpayers, the Bushes filed joint tax returns of their own.
The IRS, on reviewing the Lone Wolf McQuade and Cinema '84 returns, found deficiencies. Pursuant to TEFRA, in 1991 the IRS notified the partners of Lone Wolf McQuade that it was issuing Final Partnership Administrative Adjustments ("FPAAs") that would disallow certain deductions on the partnership's 1983-86 tax returns. See I.R.C. § 6223(a) (requiring notice to the Tax Matters Partner and to each individual partner). The IRS also notified the partners of Cinema '84 of disallowed deductions in that partnership's returns for tax years 1985-89.
Both partnerships challenged the FPAAs with petitions in the Tax Court.[1]See I.R.C. § 6226(a) (concerning judicial review of FPAAs). While proceedings were pending, on August 7, 1999, the Bushes settled with the IRS. See I.R.C. § 6224(c) (concerning settlement). The settlement papers  two Form 906 Closing Agreements on Final Determination Covering Specific Matters  expressly stated that they did not make any adjustments to partnership items. The agreements addressed the right to claim partnership losses on individual tax returns. The agreements provided that the settling partners were only entitled to claim partnership losses to the extent of their "at *1326 risk" amount. They also contained stipulations as to how to calculate the exact dollar amount for each settling partner that was "at risk" for the relevant tax years. For example, the Bushes' "capital contribution" was set at $50,000 per partnership, and the agreement stated that the at risk amount could increase with any additional capital contribution to the partnership after 1986. See Bush, 78 Fed.Cl. at 78; Bush Panel J.A. 191. Following these Closing Agreements, the Tax Court dismissed the Bushes from the partnership proceedings concerning Cinema '84 and Lone Wolf McQuade.
On July 12, 2000, the IRS issued Notices of Adjustment for the Bushes' 1985, 1986, and 1987 joint tax returns. The Notices disallowed a significant portion of the losses the Bushes had claimed connected to the two partnerships. Two weeks later, the IRS assessed the Bushes for the following amounts:


Tax Year     Assessment
1985         Tax:      $16,708.00
             Interest: $42,660.44
1986         Tax:      $10,817.00
             Interest: $46,004.97
1987         Tax:      $ 9,635.00
             Interest: $26,729.62

1986 at 79. The government argues, and the Bushes do not dispute, that these amounts were calculated based on provisions in the Closing Agreements, specifically the stipulated amount of the Bushes' at-risk capital in those years. Crucial to this appeal, the IRS did not issue the Bushes any notices of deficiency as to their joint tax returns prior to making these assessments.
The Bushes paid the assessed tax and interest the next month, August 2000. Two years later, they initiated refund proceedings with the IRS seeking to recover that payment on grounds that the IRS failed to provide them deficiency notices. The IRS denied their claims, and the Bushes filed suit in the Court of Federal Claims on October 25, 2004. Id.
The facts pertaining to case number XXXX-XXXX are largely identical. Like Mr. Bush, taxpayer Tommy Shelton was a limited partner in Cinema '84 (Lone Wolf McQuade does not figure in Mr. Shelton's appeal). Like the Bushes, Mr. Shelton filed individual income tax returns claiming deductions stemming from that partnership and so was affected by the TEFRA proceeding concerning Cinema '84. Like the Bushes, Mr. Shelton settled with the IRS. His Closing Agreement differed only in the tax years at issue and the amount of Mr. Shelton's capital contribution, which was stipulated to be $150,000. Shelton, 2007 U.S. Claims LEXIS 311, at *3.
Mr. Shelton's post-settlement experience also mirrored that of the Bushes. On July 20, 2000, the IRS issued Notices of Adjustment disallowing deductions on a number of Mr. Shelton's tax returns in the 1980s and 1990s. It subsequently assessed him as follows:


Tax Year     Assessment
1981         Tax:      $ 9,782.00
             Interest: $61,329.37
1985         Tax:      $ 9,444.00
             Interest: $35,147.78
1986         Tax:      $ 8,134.00
             Interest: $26,500.86
1987         Tax:      $ 1,346.00
             Interest: $ 3,193.01
1989         Tax:      $   811.00
             Interest: $ 1,115.49
1992         Tax:      $   958.00
             Interest: $   802.02
1995         Tax:      $ 1,891.00
             Interest: $   785.46

Id., at 89,584-85. As in the case of the Bushes, the IRS issued no Notices of Deficiency to Mr. Shelton. Mr. Shelton paid *1327 the assessed tax and interest on August 28, 2000. Like the Bushes, he initiated refund proceedings challenging the absence of a deficiency notice, but was denied as to these assessments.[2] On August 23, 2002, Mr. Shelton sued in the Court of Federal Claims.
As already noted, the cases brought by Mr. Bush and Mr. Shelton were among numerous others brought by other partners in other partnerships in essentially the same circumstances. See supra note 1. The Court of Federal Claims selected these two cases for "briefing and representative resolution." Bush, 78 Fed.Cl. at 77. There were essentially no disputed facts, and the plaintiffs and the government cross-moved for summary judgment. The plaintiffs argued that the post-settlement assessments made by the IRS were invalid because they had not been preceded by a notice of deficiency, citing the Tax Code's general deficiency notice provision. See I.R.C. § 6212(a). The government disagreed, arguing that no notice of deficiency was required because the new assessments were mere "computational adjustments" exempt from the notice requirement. See I.R.C. § 6230(a)(1).
In both cases, the Court of Federal Claims sided with the government. It held that the post-settlement adjustments were "computational adjustments" as that term is defined in the Tax Code and that none of the Tax Code provisions requiring notice even for computational adjustments applied. Bush, 78 Fed.Cl. at 83 et seq.; Shelton, 2007 U.S. Claims LEXIS 311, at *12-*13. Plaintiffs timely appealed.
A divided panel of this court affirmed, but on different grounds. Bush v. United States, 599 F.3d 1352 (Fed.Cir.2010), vacated, 400 Fed.Appx. 556 (Fed.Cir.2010). The panel majority agreed with the taxpayers that the IRS's post-settlement assessments were not "computational adjustments." Id., at 1361. Nonetheless, the majority would have affirmed, reasoning that the IRS's failure to issue notices of deficiency was harmless under the federal harmless error statute, 28 U.S.C. § 2111. Id., at 1363-66. Specifically, the majority concluded that the issuance of a notice would have conferred to the taxpayers a right to seek an injunction against the IRS's collection, and a refund of any collected amount. Because the taxpayers in this case paid voluntarily  i.e., there was no formal collection proceeding  and because no refund was ultimately owed them, the panel majority held the failure to send a deficiency notice harmless.
That opinion was accompanied by a concurrence which agreed with the panel majority's final result but disagreed with its statutory interpretation and its application of the harmless error exception. Id., at 1366-76 (Prost, J., concurring in the result). The concurrence pointed out that harmless error doctrine "was not advocated by either party in this court or below." Id., at 1373. It also cited opinions from other courts holding that failure to send a deficiency notice cannot be harmless error. Id., at 1376 (citing Phila. & Reading Corp. v. Beck, 676 F.2d 1159, 1163-64 (7th Cir. 1982); Hoyle v. Comm'r, 131 T.C. 197, 205, 2008 WL 5156596 (2008)). Rather than join the majority's expedition into harmless error analysis, the concurrence would have affirmed the Court of Federal Claims' interpretation that the assessments in this case were "computational adjustments."
We subsequently granted the plaintiffs' petitions to rehear the case en banc, vacated the panel opinion, and requested additional *1328 briefing from the parties. Bush, 400 Fed.Appx. 556. We specifically asked the parties to address four questions:
a) Under I.R.C. § 6213, were taxpayers in this case entitled to a pre-assessment deficiency notice? Were the assessments the results of a "computational adjustment" under § 6230 as the term "computational adjustment" is defined in § 6231(a)(6)?
b) If the IRS were required to issue a deficiency notice, does § 6213 require that a refund be made to the taxpayers for amounts not collected "by levy or through a proceeding in court"?
c) Are taxpayers entitled to a refund under any other section of the Internal Revenue Code? For example, what effect, if any, does an assessment without notice under § 6213 have on stopping the running of the statute of limitations?
d) Does the harmless error statute, 28 U.S.C. § 2111, apply to the government's failure to issue a deficiency notice under I.R.C. § 6213? If so, should it apply to the taxpayers in this case?
Id., at 556-57.

III
Our first task is to construe the relevant Tax Code sections to discover whether the IRS was required to issue notices of deficiency before assessing additional tax payments from the Bushes and from Mr. Shelton.
The Tax Code's general rule requiring pre-assessment notices of deficiency is set forth in I.R.C. § 6212: "If the Secretary determines that there is a deficiency in respect of any tax imposed by [various parts of the Tax Code], he is authorized to send notice of such deficiency to the taxpayer by certified mail or registered mail." Such notice is generally a prerequisite to any attempt by the IRS to assess or collect on the deficiency. Comm'r v. Shapiro, 424 U.S. 614, 618, 96 S.Ct. 1062, 47 L.Ed.2d 278 (1976).
As already mentioned, auditing partnerships raises novel considerations not present when auditing individuals. TEFRA added provisions to increase efficiency when the IRS audits partnership returns that may affect a large number of individual taxpayers. Prominent among these provisions for our purposes is § 6230, which creates special dispensation from certain administrative requirements for some partnership proceedings.
Section 6230(a) broadly exempts a class of "computational adjustments" from the notice and other administrative provisions otherwise required for a deficiency proceeding:
(a) Coordination with deficiency proceedings. 
(1) In general.  Except as provided in paragraph (2) or (3), subchapter B of this chapter shall not apply to the assessment or collection of any computational adjustment.
(2) Deficiency proceedings to apply in certain cases. 
(A) Subchapter B shall apply to any deficiency attributable to 
(i) affected items which require partner level determinations (other than penalties, additions to tax, and additional amounts that relate to adjustments to partnership items), or
(ii) items which have become nonpartnership items (other than by reason of section 6231(b)(1)(C)) and are described in section 6231(e)(1)(B).
I.R.C. § 6230(a)(1)-(2)(A).[3] Paragraphs (1) and (2), set forth above, are relevant to *1329 this appeal, and they define the two prongs of our statutory analysis. First, we hold that the IRS's adjustments in this case are "computational adjustments" covered by paragraph (1). Second, we hold that the deficiencies alleged by the IRS against Mr. Bush and Mr. Shelton are not "attributable to affected items which require partner level determinations" as per paragraph (2).

A
The Tax Code defines "computational adjustment" as:
[T]he change in tax liability of a partner which properly reflects the treatment under this subchapter of a partnership item. All adjustments required to apply the results of a proceeding with respect to a partnership under this subchapter to an indirect partner shall be treated as computational adjustments.
I.R.C. § 6231(a)(6). As already discussed, a "partnership item" is an item of a partnership return whose treatment is better handled at the partnership level than partner-by-partner. See id. § 6231(a)(3); see also 26 C.F.R. § 301.6231(a)(3)-1 (further defining "partnership item").
Plaintiffs urge that the IRS's assessment against them is not a "computational adjustment" because, in their view, a "computational adjustment" occurs only where the IRS changes some aspect of its treatment of a partnership item, and as a result the computed tax liability has changed. They point out a provision in the Closing Agreements expressly stating, "No adjustment to the partnership items shall be made...." Shelton Panel J.A. 150.
The government acknowledges that, by virtue of settlement, certain partnership items may become nonpartnership items. It emphasizes, however, that the term "computational adjustment" is defined in the Code not as requiring "changes" to partnership items, but merely treatment of such items. The government argues that any determination of partnership items in a TEFRA proceeding, including determining that the items were properly reported, constitutes "treatment" of that partnership item. Further, it argues that when a partner's tax liability "properly reflects" this treatment, then it is properly assessed as a computational adjustment.
The government also maintains that accepting the taxpayers' proposed statutory construction would frustrate the purpose of TEFRA. Specifically, the government contends that regardless of whether treatment of a partnership item changes during a TEFRA proceeding, an individual partner should not get a second opportunity to challenge that treatment following the TEFRA proceeding unless there are partner-level factual determinations involved.
Questions of statutory construction turn on "the language itself, the specific context in which the language is used, and the broader context of the statute as a whole." Robinson v. Shell Oil Co., 519 U.S. 337, 341, 117 S.Ct. 843, 136 L.Ed.2d 808 (1997). In this case, all of these support our conclusion that a "computational adjustment," as defined in § 6231(a)(6), does not require that the treatment of a partnership item change during the TEFRA proceeding.
The purpose of TEFRA is to provide a single, unified forum for determination of partnership items. Every partner is given notice of this proceeding and every partner has an opportunity to participate. I.R.C. § 6226(c). If a notice of deficiency were to be required in the circumstances urged by the taxpayers  when a TEFRA proceeding results in a change in tax liability with no changes to partnership items  then individual partners would be able to have a second pre-assessment bite at the apple, challenging the TEFRA determinations of partnership items in the Tax Court. Instead, *1330 this scenario should result in a directly assessed computational adjustment.
This is true regardless of whether the TEFRA proceeding makes changes to the treatment of partnership items from the partnership returns. Indeed, if the IRS, in a TEFRA proceeding, accepts the partnership return as fully correct, it may still make assessments as computational adjustments for any changes in tax liability that arise from the partnership proceeding. The plain language of the statute demands this result. The word "change" in the statute modifies "the tax liability of a partner." The word "treatment" modifies the phrase "of a partnership item." This structure is incompatible with plaintiffs' contention that a change to "treatment" of a partnership item is a prerequisite to any computational adjustment. What must change is the partner's tax liability, not necessarily the treatment of any partnership item. To hold differently would be grammatically indefensible. Further, the word "treatment" is not a synonym for "change." The word "treatment" is broad, but understandably so, given that the tax code performs an enormous set of functions  from categorizing items as "income" or "loss," to determining whether an item warrants a tax credit, deduction, or additional tax. It is thus not surprising that Congress has used "treatment" often, but not because it really meant "change." See, e.g., id. §§ 1361-1379 (subchapter S, "Tax Treatment of S Corporations and Their Shareholders"), § 4462, §§ 6211-6234 (subchapter C, "Tax Treatment of Partnership Items"). There is no evidence that Congress intended the phrase "treatment under this subsection of a partnership item" to mean less than its naturally broad and inclusive meaning. Cf. Reiter v. Sonotone Corp., 442 U.S. 330, 338-39, 99 S.Ct. 2326, 60 L.Ed.2d 931 (1979). To interpret "treatment" to mean "change [in treatment]" would fail to give proper weight to the words chosen by Congress. See Sosa v. Alvarez-Machain, 542 U.S. 692, 711 n. 9, 124 S.Ct. 2739, 159 L.Ed.2d 718 (2004) ("[W]hen the legislature uses certain language in one part of the statute and different language in another, the court assumes different meanings were intended.") (internal quotation marks omitted). Had Congress intended to limit "computational adjustments" to tax liability changes arising from changes in treatment of a partnership item, it could have used the word "change" or "change in treatment" rather than the word "treatment" alone.
Our reasoning in Olson v. United States supports this conclusion. 172 F.3d 1311 (Fed.Cir.1999). Olson holds that assessments are "computational adjustments" when they require "no individualized factual determinations" as to the correctness of the original partnership items or "any other factual matters such as the state of mind of the taxpayer upon filing." Id., at 1318. Under Olson, when critical questions of fact have been resolved, then "application of that stipulated fact to the tax returns in question requires only computational action." Id., This applies with equal force to settlements as to fully contested TEFRA determinations. And, in fact, other courts have adopted our approach when the only remaining issue after a TEFRA proceeding is to apply a mathematical formula. See, e.g., Desmet v. Comm'r, 581 F.3d 297, 303-04 (6th Cir.2009); Callaway v. Comm'r, 231 F.3d 106, 110 & n. 4 (2d Cir.2000) (holding that "where no further factual determinations are necessary at the partner level, an assessment attributable to an `affected item' may also be made by computational adjustment" because determining the tax liability "is a mathematical calculation and requires no further factual finding"). Olson supports our conclusion because, under its rule, a post-settlement adjustment is "computational" because after the settlement, there is nothing left to *1331 do but perform a calculation to determine tax liability. That is precisely the case here.
Plaintiffs' remaining arguments are not persuasive. They point to § 6230(a)(2)(A)(i) and contend that our interpretation would render a wide variety of assessments  even those based on individual partner-level factual determinations  "computational adjustments." As shown above in our discussion of Olson, and in the additional analysis below, we agree with taxpayers that any tax liability that arises based on individual partnerlevel factual determinations requires a notice of deficiency. That is not the situation in this case.
Similarly, plaintiffs argue that our holding would render the second sentence of I.R.C. § 6231(a)(6) (the definition of "computational adjustment") superfluous. This sentence reads "[a]ll adjustments required to apply the results of a proceeding with respect to a partnership under this subchapter to an indirect partner shall be treated as computational adjustments." Because they mistakenly believe that the government's proposed interpretation would make every assessment a computational adjustment, plaintiffs argue that such an interpretation must be rejected in order to avoid making the above-cited sentence superfluous. We dispute plaintiff's premise. To hold, as they suggest, that assessments based on detailed partner-level determinations are nevertheless "computational" would be incompatible with the statute, and we do not so hold. We thus find the second sentence of § 6231(a)(6) entirely compatible with our holding that a "computational adjustment" can arise from a change to tax liability properly reflecting treatment of a partnership item, even where that treatment does not change during the TEFRA proceeding.
Further, the taxpayers argue that our holding conflicts with the applicable regulation on computational adjustments which reads:
A change in the tax liability to properly reflect the treatment of a partnership item under subchapter C of chapter 63 of the Code is made through a computational adjustment. A computational adjustment may include a change in tax liability that reflects a change in an affected item where that change is necessary to properly reflect the treatment of a partnership item.... However, changes in a partner's tax liability with respect to affected items that require partner-level determinations (such as a partner's at-risk amount that depends upon the source from which the partner obtained the funds that the partner contributed to the partnership) are not included in a computational adjustment.
Temp. Treas. Reg. § 301.6231(a)(6)-1T, 52 Fed.Reg. 6,779, 6,790-91 (Mar. 5, 1987).[4] The taxpayers argue that this regulation shows that a computational adjustment must involve some change in treatment of a partnership item. We disagree. Nothing about this regulation requires that a computational adjustment involve a change in treatment of a partnership item. While it shows that a computational adjustment may (and often does) result from a change in treatment of a partnership item, nothing in the regulation demands that this be the only scenario.
The taxpayers then argue that, contrary to the government's assertion, I.R.C. § 6222(c) actually supports their definition of computational adjustment. This section states that certain assessment restrictions "shall not apply to any part of a deficiency attributable to any computational adjustment required to make the treatment of *1332 items by such partner consistent with the treatment of the items on the partnership return." Taxpayers argue that this statutory section defines an exception to the general rule that a computational adjustment requires a change in treatment to a partnership item. We are not persuaded that this section has such an effect. This section merely makes clear that the assessment of computational adjustments goes in both directions, applying both to changes in tax liability that result from the TEFRA proceeding itself and to changes in tax liability that arise from making a partner's tax return consistent with the TEFRA proceeding and the partnership return.
Finally, the taxpayers argue that theirs are not computational adjustments because the definition of "computational adjustment" is located in a separate statutory chapter than the definition of amounts at risk. Compare I.R.C. § 465 ("Deductions limited to amounts at risk.") (Chapter 1, Subchapter E) with I.R.C. § 6231(a) (setting forth definitions, including for "computational adjustment," "for purposes of this subchapter") (Chapter 63, Subchapter C). We disagree with the plaintiffs. The at-risk amount, in the context of a partnership, is an affected item, meaning it has a partnership component. As long as the limitation on the at-risk amount relates to treatment of a partnership item, as in this case, it can be assessed as a computational adjustment.
In this case, the IRS believed that the taxpayers were not entitled to claim certain losses. Had the TEFRA proceeding gone through to completion and the IRS prevailed, the claimed losses would have been invalid and the IRS would have undisputedly assessed the taxes via a computational adjustment. Instead, plaintiffs chose to settle. They agreed to formulas to determine their at-risk amount, which necessarily affected the amount of loss they could claim on their personal returns. The only reason there were not "changes" to partnership items is because of the way the parties structured their settlements. That does not mean, however, the settlements failed to give rise to a "change in tax liability of a partner which properly reflects the treatment ... of a partnership item." These settlements took disputes as to partnership items and resolved them by translating those partnership items into specific numbers or computations. As a result, the IRS's post-settlement assessments reflect nothing more than simple computational adjustments stemming from those agreements.
The taxpayers effectively admit that this is the situation in the present case by acknowledging that, rather than requiring complex factual determinations, the Closing Agreements in question "establish ... the formula for computing each of [the taxpayer's] at risk amounts after 1986." Bush Panel Appellant's Br. 43; see also, Shelton Panel Appellant's Br. 45. This admission makes it clear that under our construction, the assessments were the result of computational adjustments. After the settlement, there was nothing to do other than plug numbers into a formula to determine any change in tax liability. Thus, the assessments were computational adjustments under I.R.C. § 6231.

B
Our holding that the assessments in this case meet the definition of "computational adjustment" under I.R.C. § 6231(a)(6) does not end our analysis. Notices of deficiency would still be due for any deficiencies (including any that would otherwise be a computational adjustment) attributable to "affected items which require partner level determinations" under § 6230(a)(2)(A)(i).
*1333 An "affected item" is "any item to the extent such item is affected by a partnership item." I.R.C. § 6231(a)(5). An affected item includes two parts, a partnership component and a nonpartnership component, with the former affecting the latter. See Keener, 76 Fed.Cl. at 460.
Taxpayers argue that the at-risk amounts determined by the settlements in this case involved partner-level factual determinations that triggered the notice requirement. For example, they argue that the "settlements acknowledged that the partnership debt was valid and agreed that their amounts at-risk would be reduced by any portion of that debt they had individually assumed  clearly a partner-level determination." En Banc Appellants' Br. 6, n. 9.
The government responds that the determination of tax liability in these cases involved no partner-level factual determinations. While it concedes that a partner's at-risk amount nominally has nonpartnership elements, the government argues that these cases actually turned on partnership-level considerations. The government states:
Generally, a taxpayer is at risk for amounts contributed to a partnership, and borrowed by the partnership where there is recourse against the taxpayer for the repayment of the borrowed amounts and the taxpayer is not otherwise shielded from personal liability. Whether a partnership note is recourse or nonrecourse is a partnership item. Here, the IRS determined in the FPAAs that, contrary to the partnership returns, the partnership notes were nonrecourse. This proposed change to a partnership item indisputably would have resulted in computational adjustments reducing taxpayers' at-risk amounts. The closing agreements reached the same result.
En Banc Appellee's Br. 33 (citations omitted). The government argues that the settlements resolved only partnership items and thus could be directly assessed as a computational adjustment without the need for a deficiency notice.
We agree with the analysis of the Court of Federal Claims that, while the at-risk amount may be an affected item with a nonpartnership component, in these cases there were no partner-level determinations. The Court of Federal Claims noted that "a settlement is usually applied to a partner by means of a computational adjustment and not under the ordinary deficiency and refund procedures." Bush, 78 Fed.Cl. at 81 (quoting Bob Hamric Chevrolet v. United States, 849 F.Supp. 500, 510 (W.D.Tex.1994)). The settlements between the taxpayers and the IRS only required computation to determine the taxpayers' at-risk amount and thus their tax liability. Specifically, in paragraph 3 of the Closing Agreement, the taxpayers agreed that the at-risk amount would be "their capital contribution to the partnership." Shelton Panel J.A. 150. The next paragraph identifies that capital contribution as $150,000. Id., The remaining paragraphs define the ways in which this at-risk amount may change. For example, paragraph 7 states "[t]o the extent the taxpayers make additional cash contributions to the capital of the partnership after 1989, the taxpayers' amount at risk will be increased in accordance with I.R.C. § 465." Id.,
Simply because these at-risk amounts may be specific to the individual partner does not mean that they are partner-level determinations within the meaning of § 6230(a)(2)(A)(i). As in Olson, all that remained after the settlements was to apply the values from the taxpayers' returns to the stipulated computations in the settlement agreement and directly assess the tax. There was no need to collect any *1334 additional information from the taxpayers or make any factual determinations.
As the Court of Federal Claims noted, a notice of deficiency is due under I.R.C. § 6230(a)(2)(A)(i) only when "uncertainty as to factual matters must be resolved before arriving at a figure for those affected items." Bush, 78 Fed.Cl. at 83 (citing Olson, 172 F.3d at 1317). There are several types of such factual determinations that have been outlined in earlier cases. For example, in some instances the IRS may issue a penalty for negligently under-reporting a partner's share of a partnership's tax liability. Bob Hamric Chevrolet, 849 F.Supp. at 511. This requires a factual inquiry into the taxpayer's negligence and cannot be assessed without a notice of deficiency. Id. Another example is when the taxpayer and a third party have an agreement for the assumption of certain tax liabilities. Id., This would require the IRS to make a factual determination regarding these assumed liabilities and would entitle the taxpayer to a notice of deficiency. It is clear that none of these factual determinations had to take place in this case in order to determine tax liability from the settlement terms. The IRS simply had to plug the numbers from the taxpayers' tax returns into the computations set out in the Closing Agreements and directly assess any change in tax liability. As noted above, the taxpayers conceded as much in their opening briefs when they admitted that the Closing Agreements simply "establish ... the formula for computing each of [the taxpayer's] at risk amounts after 1986." Bush Panel Appellant's Br. 43; see also, Shelton Panel Appellant's Br. 45.
In conclusion, we affirm the judgments of the Court of Federal Claims. The changes in tax liability that arose from the Closing Agreements in this case were computational adjustments under I.R.C. § 6231(a)(6). Further, to the extent that the at-risk amounts were affected items, they did not require any partner-level factual determinations. Thus, the IRS was correct to directly assess these taxes without a notice of deficiency.

IV
Because we conclude that the assessments in this case amounted to computational adjustments, no deficiency notices were necessary. The three remaining questions this court put to the parties as part of en banc rehearing each presumed that a deficiency notice was required. Because our holding here definitively contradicts that presumption, we need not analyze those questions. We therefore affirm the judgment of the Court of Federal Claims.
AFFIRMED
DYK, Circuit Judge, dissenting, with whom Circuit Judges NEWMAN, LINN, and REYNA join.
The majority holds that a deficiency notice under I.R.C. § 6230 was not required because the assessment here involved a "computational adjustment," as defined by I.R.C. § 6231(a)(6), and no individual partner level determinations were necessary. In my view, the majority has effectively rewritten the statute to virtually eliminate the requirement that the government establish the existence of a computational adjustment. I respectfully dissent.
In most cases, the IRS is barred from assessing and collecting taxes unless it has sent the taxpayer a notice of deficiency. Id., § 6213(a). The notice allows the taxpayer to contest the amount due before collection proceedings are initiated and to elect to litigate the merits of the alleged deficiency assessment in the Tax Court. However, the Code dispenses with the deficiency notice requirement when the assessment is merely conforming the taxpayer's individual calculation of tax liability to *1335 a partnership's treatment of partnership items (i.e., a "computational adjustment"). Id., § 6230(a)(1). The Code, however, also creates an exception to this exception where the treatment of a partnership item changes the taxpayer's tax liability, but the tax computation still requires a determination of a partner level issue, that is, a non-partnership item.[1] The Code provides that a deficiency notice is required if the assessment is "attributable to ... affected items which require partner level determinations (other than penalties, additions to tax, and additional amounts that relate to adjustments to partnership items)." Id., § 6230(a)(2)(A)(i).[2] Thus, for there to be an exemption from the deficiency notice requirements, § 6230(a) imposes not only a requirement that there be a computational adjustment, but also a requirement that there not be an "affected item[ ] ... which require[s] partner level determinations." Id.,
Focusing on the "computational adjustment" issue, the Code here defines that term as "the change in the tax liability of a partner which properly reflects the treatment under this subchapter of a partnership item." Id., § 6231(a)(6). The IRS may directly assess any "computational adjustment required to make the treatment of the items by such partner consistent with the treatment of the items on the partnership return." Id., § 6222(c) (emphasis added). The need to conform the individual return to the treatment of a partnership item may arise in either of two ways  either because the individual taxpayer return does not accurately reflect partnership items in the partnership return, or because a TEFRA proceeding results in a different treatment of a partnership item than in the original return. As the Second Circuit noted in Callaway v. Comm'r, 231 F.3d 106, 109-10 (2d Cir. 2000):
Such peremptory adjustments of a partner's return [(i.e., assessments made without a deficiency notice)] are justified because the partner will already have benefitted from notice of and the right to participate in any proceeding under the TEFRA provisions to determine the partnership items at the partnership level. The IRS may adjust partnership items only at the partnership level and only after following the TEFRA procedures.... After the FPAA adjustments [following the TEFRA procedures] become final ..., the IRS may assess partners with the tax which properly accounts for their distributive share of the adjusted partnership items, without notice, as a computational adjustment.
There is no claim here that the individual taxpayers' computations failed to reflect the treatment of a partnership item in the partnership return. Nor did the TEFRA proceeding result in any change in the *1336 treatment of a partnership item. The settlement agreement of the TEFRA proceeding stated specifically: "No adjustment to the partnership items shall be made ... for purposes of this settlement." The fact that there might have been a computational adjustment as a result of the TEFRA proceeding if the partnership losses had been disallowed hardly suggests that a computational adjustment was involved when the parties decided not to make a change to any partnership item. Thus, the "change in liability" of the taxpayer partners did not result from the "treatment ... of a partnership item" but from a change in the treatment of an individual partner level item in the settlement agreement (i.e., the agreement to cap the at-risk amount of the individual partners). Because no partnership item is involved, there can be no computational adjustment.
The majority makes little effort to come to grips with the statutory language defining a "computational adjustment." Rather, the majority reasons that, "when critical questions of fact have been resolved, the `application of that stipulated fact to the tax returns in question requires only computational action.'" Maj. Op. at 1330 (quoting Olson v. United States, 172 F.3d 1311, 1318 (Fed.Cir.1999)). But the stipulated facts (or those established in the TEFRA proceeding) must relate to a partnership item, not to an individual partner item. Here, the settlement agreement by its own explicit terms changed only the partner level at-risk amount. The settlement agreement explicitly stipulated that "[n]o adjustment to the partnership items shall be made ... for purposes of this settlement." Because the settlement agreement then adjusted the at-risk amount, it clearly did not view the at-risk amount as a "partnership item[ ]."
The taxpayers correctly point out that the majority's approach effectively dispenses with the requirement of a deficiency notice when the change in tax liability is not the result of a change in treatment of a partnership item but results from a change in an individual partner item. The majority's answer is that § 6230(a) still requires notice if an "affected item ... require[s] partner level determinations" (i.e., if there is an unresolved factual issue concerning individual partner liability). There is none here, says the majority, because the taxpayers stipulated to the at-risk amount, and the tax liability may be calculated by applying this stipulation to the tax payers' individual returns. But that is not all the statute says. To be exempt from the deficiency notice requirements, § 6230(a) imposes the additional requirement that there be a computational adjustment. See I.R.C. § 6230(a)(1).
The majority remarkably finds support in two decisions by the Second and Sixth Circuits in Callaway, 231 F.3d at 110 n. 4, and Desmet v. Comm'r, 581 F.3d 297, 303-04 (6th Cir.2009), suggesting that these circuit decisions have similarly held that post-settlement adjustments were "computational" when there was "nothing left to do but perform a calculation to determine tax liability." Maj. Op. at 1331, 1330-31. The majority appears to think that these cases suggest that if an item is not an "affected item" requiring a partner level determination, then it necessarily follows that it is a "computational adjustment." But neither of these cases suggests that the mere fact that there is not an affected item requiring a partner level determination could dispense with the additional requirement that there be a computational adjustment. Both of these cases acknowledge that there must be a computational adjustment in addition to the separate requirement imposed by § 6230(a)(2)(A)(i) that there be no "affected item[] ... which require[s] partner level determinations."
*1337 The majority appears to be concerned that applying the statute as written will allow taxpayers to relitigate issues resolved by settlement agreements. The basis for this concern is difficult to fathom. A settlement agreement is binding; the requirement of a deficiency notice does nothing to undo such an agreement. It merely requires that the taxpayer receive notice of how the application of the settlement agreement will affect the taxpayer's tax liability. A right to a deficiency notice has nothing to do with whether there is merit to the taxpayer's underlying claims.
Because I conclude that a "computational adjustment" was not involved, I need not reach the additional question of whether there was an "affected item" involved requiring a partner level determination. If I am correct that a deficiency notice was required, the question then becomes whether the taxpayers are entitled to a refund because a deficiency notice was not provided. For the reasons stated in the original panel opinion, and as the government agrees, § 6213(a) only provides for an automatic refund in circumstances where the tax is "collected" during a period in which "collecti[on] by levy or through a proceeding in court" is prohibited. In this case, the IRS never initiated collection proceedings against the taxpayers. Indeed, the taxpayers voluntarily paid the assessments and then sued for a refund. The taxpayers do not contend that the amounts paid were not owed if the limitations period had not run when payment was made. If the statute of limitations had not run when the payments were made, the fact that the IRS failed to issue the notice required before the IRS could have assessed or collected the tax does not require a refund. See Lewis v. Reynolds, 284 U.S. 281, 283, 52 S.Ct. 145, 76 L.Ed. 293 (1932) ("An overpayment must appear before refund is authorized."); cf. Jones v. Liberty Glass Co., 332 U.S. 524, 531, 68 S.Ct. 229, 92 L.Ed. 142 (1947) ("[T]he payment of more than is rightfully due is what characterizes an overpayment."). Our sister circuits have applied Lewis for the principle that the timely payment of taxes properly due is not an overpayment, regardless of whether a timely assessment has been made. See, e.g., Williams-Russell & Johnson Inc. v. United States, 371 F.3d 1350, 1353 (11th Cir.2004) (applying the principles in Lewis and finding "no convincing legal reason why [the taxpayer] should be allowed to recover what it owed and has already properly paid simply because the IRS was lax in it[s] responsibilities" and noting that "it would be nonsensical to allow a taxpayer to recover those taxes now"). However, the government agrees that the running of the statute of limitations before payment may compel a refund. I would remand this case to the Claims Court to address this issue.
NOTES
[*]  Circuit Judge Gajarsa assumed senior status on July 31, 2011.
[1]  In fact, both partnerships had the same Tax Matters Partner, Richard Greenberg. The Lone Wolf McQuade and Cinema '84 partnerships are known colloquially as "Greenberg Brothers partnerships" in recognition of the role of the Greenberg Brothers Partnership in their marketing. See Bush, 78 Fed.Cl. at 77. There are a substantial number of other Greenberg Brothers partnerships, and approximately thirty have brought tax refund suits similar to the two in this appeal. Id.,
[2]  Mr. Shelton did obtain refunds for certain assessments not discussed herein. Shelton, 2007 U.S. Claims LEXIS 311, at *8-*9.
[3]  The references to "subchapter B" in paragraphs (1) and (2) mean Chapter 63, Subchapter B of the Tax Code, which contains the notice statute.
[4]  There is a more current version of this regulation. See 26 C.F.R. § 301.6231(A)(6)-1. It does not vary from this version in any substantive way that would affect our analysis.
[1]  Section 6230(a) provides, in relevant part:

(a) Coordination with deficiency proceedings. 
(1) In general.  Except as provided in paragraph (2) or (3), subchapter B of this chapter [requiring a deficiency notice] shall not apply to the assessment or collection of any computational adjustment.
(2) Deficiency proceedings to apply in certain cases. 
(A) Subchapter B shall apply to any deficiency attributable to 
(i) affected items which require partner level determinations (other than penalties, additions to tax, and additional amounts that relate to adjustments to partnership items), or
(ii) items which have become nonpartnership items (other than by reason of section 6231(b)(1)(C)) and are described in section 6231(e)(1)(B).
I.R.C. § 6230(a) (emphases added).
[2]  An "affected item" is defined as "any item to the extent such item is affected by a partnership item." Id., § 6231(a)(5).
