
129 P.3d 919 (2006)
JOHN'S HEATING SERVICE, Appellant,
v.
Michael A. LAMB and Cynthia E. Johnson-Lamb, Appellees.
No. S-11228.
Supreme Court of Alaska.
February 24, 2006.
*920 Michael D. Corey, Sandberg, Wuestenfeld & Corey, Anchorage, for Appellant.
Sarah J. Tugman, Sarah J. Tugman, Attorney at Law, Anchorage, for Appellees.
Before: BRYNER, Chief Justice, MATTHEWS, EASTAUGH, FABE, and CARPENETI, Justices.

OPINION
EASTAUGH, Justice.

I. INTRODUCTION
The Lambs sued John's Heating Service in December 1993, alleging that it failed to repair their furnace during an October 1991 service call or warn them of the dangers it posed, causing them to suffer carbon monoxide poisoning. A jury found for the Lambs, but in John's Heating's first appeal we remanded for application of the discovery rule to determine whether the two-year statute of limitations barred the Lambs' claims.[1] The superior court concluded on remand that the lawsuit was timely. John's Heating appeals from that conclusion. We affirm. Undisputed findings of fact on remand establish that before early 1993 the Lambs did not know and were not on notice that their furnace might be a cause of their symptoms of impairment. Given those findings, it cannot be said that the Lambs were on inquiry notice before early 1993. Because they had at least two years after early 1993 in which to file suit, their December 1993 complaint was timely.

II. FACTS AND PROCEEDINGS
This is the second time we have considered the timeliness of the lawsuit brought by Michael Lamb and Cynthia Johnson-Lamb against John's Heating Service.[2] Many of *921 the historical facts are set out in our first opinion and some were presented to the superior court on remand.
The Lambs moved into a house in Kodiak in August 1991.[3] On October 15 they called John's Heating to inspect their furnace, and on the same day John's Heating sent Tim Galloway to investigate the problem.[4] The Lambs allegedly told Galloway that the furnace was not functioning properly, that it seemed to be circulating soot throughout the house, and that they were concerned about the persistent smell of fuel in the house.[5] Galloway leveled the fuel tank and relit the furnace, but did nothing more.[6] The Lambs began to suffer physical ailments from what their complaint later alleged was carbon monoxide poisoning caused by the furnace.[7] The Lambs continued to live in the house and use the furnace until January 31, 1993, when John Cloudy, a furnace repairman for another service company, responded to Cynthia Lamb's call after the furnace "started making a racket." After inspecting the furnace, Cloudy told the Lambs that the furnace was probably circulating carbon monoxide throughout the house, and that the situation could be dangerous.[8] He suggested that their problems might be related to carbon monoxide and that they should see a doctor.
The Lambs promptly replaced their furnace but continued to suffer problems that they later attributed to chronic carbon monoxide exposure.[9] They hired a lawyer and in March an investigator photographed the furnace for them; they shipped it to an out-of-state expert. They were seen by a neurologist and a neuropsychologist in Anchorage in March. The resulting reports arguably found some mental impairment but were either inconclusive about whether exposure to carbon monoxide was a cause of any impairment, or expressed no firm conclusion on that topic and suggested more testing.
In mid-November 1993 a Georgia neuropsychologist recommended more tests because he thought the March examinations strongly indicated carbon monoxide inhalation for both Lambs. The Anchorage neuropsychologist performed more tests in late November, including those the Georgia expert recommended. Upon review of the new test results, the Georgia expert, by letter of December 10, expressed his opinion that the test results "show clear and convincing signs" of neurocognitive and neurobehavioral impairment as a consequence of carbon monoxide exposure.
The Lambs filed suit against a number of defendants, including John's Heating, on December 23, 1993.[10] They claimed that John's Heating negligently failed to repair their furnace or warn them of its dangerous condition.[11] John's Heating raised a statute of limitations defense, which the trial court rejected by entering partial summary judgment for the Lambs and against John's Heating.[12]
Trial followed. The jury returned a verdict for the Lambs. John's Heating appealed, raising various issues, including the statute of limitations issue.[13] Because we concluded that there was an unresolved, disputed issue of fact as to when the statute of limitations began to run, we vacated the Lambs' partial summary judgment on the statute of limitations issue and remanded for further proceedings.[14] We stated that the earliest possible "inquiry notice" date for accrual of the cause of action was October 15, 1991 (when Galloway made his service call) and that the latest possible actual notice date was January 31, 1993 (when *922 Cloudy told them the furnace was probably circulating carbon monoxide).[15]
On remand, the superior court conducted an evidentiary hearing and held that the suit was timely. Its order contained these findings of fact:
The Lambs' injuries were latent. They evolved over a period of time, as is characteristic of carbon monoxide (CO) poisoning. At some point they were on inquiry notice that there was a problem. However, they were unsuccessful in discovering the cause of their injury until the spring of 1993.
They did not connect their symptoms and the CO until Mr. Cloudy told them of CO risk in January 1993, and their doctor, with that new information, said CO could cause the otherwise unexplained symptoms.
The Lambs were on inquiry notice about soot problems from the furnace much earlier. However, the key to this case is the brain injury from CO exposure. That injury must be connected to the furnace for the elements of the tort to be reasonably known, and therefore for the statute to run. This is not a case about a dirty house; it is about brain damage.
The Lambs diligently sought medical advice about their developing symptoms. No question has been raised in that regard. The ultimate issue is whether it was reasonable for them not to have connected their injury to the furnace.
The superior court also found that:
It is not reasonable to expect the Lambs, in the early 1990s, to make a causal connection between the irritations of having an old and sooty furnace, and the mysterious symptoms that evolved over a lengthy period of time. They consulted doctors, they had the furnace checked, but there was no reason to reasonably suspect they were connected. The evidence is clear that CO poisoning in homes was not a well-understood issue in the early 1990s. Hindsight does not change this.
Having made these findings, the court then stated: "The Lambs were on inquiry notice more than two years before suit was filed in December 1993. However, their inquiry was reasonable, but unsuccessful until January of 1993. The statute began to run at that time, and suit was filed well within the limitations period." The superior court did not determine the precise date of inquiry notice.
The superior court concluded that "[t]he matter was brought within the statute of limitations."
John's Heating appeals.

III. DISCUSSION

A. Standard of Review
We review findings of fact under the clearly erroneous standard.[16] A finding is clearly erroneous if, "after a review of the entire record, we are left with a definite and firm conviction that a mistake has been made."[17] In reviewing factual findings, we view the evidence in the light most favorable to the prevailing party below.[18]
"This court applies its independent judgment in reviewing a lower court's application of law to undisputed facts."[19]


*923 B. The Superior Court Did Not Err in Concluding that the Lambs' Complaint Was Timely.

1. John's Heating's argument
John's Heating contends that the superior court committed legal error on remand and that its findings of fact establish as a matter of law that the lawsuit is time-barred by the applicable two-year statute of limitations, AS 09.10.070(a).[20] John's Heating does not challenge the superior court's fact findings establishing that the Lambs did not know before January 1993 that the furnace might be responsible for their symptoms and that their prior inquiry was reasonable. It instead advances a more subtle and complex attack. Relying on the superior court's statement that the Lambs were put on inquiry notice more than two years before they filed suit,[21] it reasons that our case law and remand instructions obliged the superior court to determine whether the interval between January 1993 and the second anniversary of the inquiry notice date allowed a reasonable time in which to file suit. It asserts that it is entitled to judgment because the superior court could not have made the findings that would have been necessary to render the Lambs' complaint timely. Thus, John's Heating reasons that the court would have been required to find that the Lambs had reasonable time in which to sue between January 1993, when their inquiry became successful, and the second anniversary of the inquiry notice date. Although John's Heating does not specify the date when it thinks the Lambs were put on inquiry notice, it necessarily assumes that it was more than two years before December 23, 1993, when the Lambs filed suit.
John's Heating derives its multi-part analysis from Cameron v. State[22] and John's Heating Service v. Lamb.[23]
To support its contention that the Lambs exceeded the reasonable time for filing suit, John's Heating asserts that eight and one-half months (the interval between the January 31, 1993 revelation and the second anniversary of Galloway's October 15, 1991 service call) left the Lambs "plenty of time" in which to sue. It refers us to a March 15, 1993 letter written by the Lambs' lawyer notifying a realty company that the Lambs intended to bring claims for exposure to carbon monoxide in the house. From this John's Heating reasons both that the Lambs had the assistance of counsel months before the complaint was filed and that their lawyer "understood the instrument of harm." It also asserts that the Lambs bore the burden on the issue but failed to explain why they did not file suit before December 23, 1993.

2. The discovery rule in Alaska
Resolution of John's Heating's contentions requires us to apply our iteration of the discovery rule. As we described that rule in Cameron and John's Heating I, if an element of a cause of action is not immediately apparent, the discovery rule determines when the statute of limitations begins to run. Our discovery rule also potentially determines whether, and for how long, the running of the statute may be tolled. It therefore may also determine whether an action is timely even if suit was filed more than two years after the cause of action accrued and the statute began running. As we described it in Cameron, our discovery rule provides that:
(1) a cause of action accrues when a person discovers, or reasonably should have discovered, the existence of all elements essential to the cause of action;
(2) a person reasonably should know of his cause of action when he has sufficient information to prompt an inquiry into the cause of action, if all of the essential elements *924 of the cause of action may reasonably be discovered within the statutory period at a point when a reasonable time remains within which to file suit.[[24]]

Cameron also enunciated a "third part" to the discovery rule.[25] It comes into play "where a person makes a reasonable inquiry which does not reveal the elements of the cause of action within the statutory period at a point where there remains a reasonable time within which to file suit." In those circumstances, "the limitations period is tolled until a reasonable person discovers actual knowledge of, or would again be prompted to inquire into, the cause of action."[[26]]
John's Heating's argument here hinges on the assumption that, as a result of the superior court's apparent determination that the Lambs were on inquiry notice before December 22, 1991, the two-year statute of limitations had run before the Lambs filed suit. It also hinges on the contention that the superior court did not make the requisite findings for applying the third part of the discovery rule, and could not have done so. John's Heating concludes that because the third part of the discovery rule therefore did not apply, the two-year statutory limitations period, having been triggered by inquiry notice before December 22, 1991, could not be extended to December 23, 1993.
John's Heating's argument requires understanding of our remand instructions in John's Heating I after we held that it was error to grant summary judgment to the Lambs on the statute of limitations issue.[27] We reasoned that John's Heating had created a genuine issue of material fact about whether the Lambs were on inquiry notice before December 22, 1991.[28] We therefore remanded and instructed the superior court to "first determine whether the Lambs had sufficient information to alert a reasonable person to begin an inquiry before December 22, 1991."[29] If so, the court was to determine whether the third part of the discovery rule applies.[30] If the superior court were to find on remand both that the Lambs had been on inquiry notice before December 22, 1991 and that the third part of the discovery rule did not apply to toll the statute of limitations, the statute would bar their claims.[31] But if the superior court were to find otherwise, the jury verdict and award were to stand, subject to our other rulings that are not at issue in the present appeal.[32]

3. The findings of fact on remand establish that the Lambs were not on inquiry notice before early 1993; their December 1993 complaint was therefore timely.
John's Heating's appellate arguments presuppose that the Lambs were on inquiry notice before December 22, 1991. Alaska Statute 09.10.070(a) gave them two years in which to sue after their cause of action accrued.[33] An unqualified determination that a plaintiff was on inquiry notice on a particular date would normally mean that the applicable statute of limitations began running on that date.[34]
The Lambs respond that they were not on inquiry notice before December 22, 1991 and *925 that John's Heating is mistaken in reading the superior court's ruling to have held that they had inquiry notice sufficient to start the statute running before December 22, 1991. They assert that "[a] review of the trial court's entire order and its reasoning, and the specific factual findings, illustrates that while the Lambs knew at that point that their furnace burned dirty, they did not have the kind of `information which is sufficient to alert a reasonable person to begin an inquiry to protect his rights.'"[35] They contend that we require, or should require, that the information needed for inquiry notice is "knowledge of some appreciable injury and at least some idea of how it might have been caused."
John's Heating argues in reply that the Lambs are really attempting to challenge the superior court's factual finding on remand that they were on inquiry notice more than two years before they filed suit. It also asserts that they are bound by that finding of fact because they have not cross-appealed, because the finding is not clearly erroneous, and because in John's Heating I this court recognized that there was a genuine issue of fact about whether the Lambs were on inquiry notice more than two years before they sued.
The absence of a cross-appeal does not prevent appellate consideration of the Lambs' response. The Lambs raise a valid issue about exactly what the superior court ruled. And even if their appellate position required us to consider whether the superior court clearly erred, they seek an affirmance of the judgment; they can properly argue that the superior court reached the right result for the wrong reason with respect to issues litigated below.[36]
Nor did we say anything in John's Heating I that forecloses the Lambs' response. We there discussed a genuine issue of fact in context of the summary judgment originally entered against John's Heating on the statute of limitations issue, and remanded so the superior court could conduct an evidentiary hearing on the issue before deciding the timeliness dispute.[37] We did not prevent, or intend to prevent, any party from contending in a subsequent appeal that the superior court's remand findings on the issue were clearly erroneous.
We therefore turn to the superior court's comments regarding the inquiry notice issue. The Lambs in essence contend that the superior court's determination that they had been on inquiry notice of soot problems was not a determination that they had been on inquiry notice of a possible chronic carbon monoxide exposure claim. That reading of the court's decision is plausible. The court stated that "[a]t some point they were on inquiry notice that there was a problem.... The Lambs were on inquiry notice about soot problems from the furnace much earlier." (Emphasis added.) Because the Lambs moved into the house in August 1991, and Tim Galloway's visit was in October 1991, the court appears to have been distinguishing between what it called "inquiry notice about soot problems" and the sort of inquiry notice that is legally significant. The court added that "[t]his is not a case about a dirty house; it is a case about brain damage." It also described the Lambs' diligence in inquiring, the reasonableness of their inquiry, and their lack of success in discovering a possible causal relationship before January 1993, at the earliest. Thus, when the court stated that "[t]he Lambs were on inquiry notice more than two years before suit was filed in December 1993," the court may have been referring to their notice of cleanliness problems and their symptoms, not to notice that caused the statute of limitations to begin running. This reading is also consistent with the superior court's statement that the two-year statute of limitations began to run in January 1993. Had the court truly meant to rule that inquiry notice predated December 22, 1991, it would have been incorrect to have concluded that the statute first began to run in January 1993. Instead, as John's Heating contends, it would have been necessary to decide whether the Lambs filed suit within a *926 reasonable amount of time after they learned the elements of their claim (sometime in 1993).[38]
But even if the superior court's "inquiry notice" comments are read as John's Heating reads them, they do not justify reversal here. There is no reason to think that the superior court's undisputed findings of fact, quoted above in Part II, about what the Lambs did, the reasonableness of their inquiry, and their lack of success until January 1993 at the earliest, were clearly erroneous.[39] Those findings of fact would not be consistent with a legal conclusion that the Lambs were on inquiry notice before December 22, 1991. Those facts establish that the Lambs did not, before January 1993, have enough information to alert them that they had a potential cause of action for their symptoms. Hence, the Lambs were put on inquiry notice of their cause of action no earlier than January 31, 1993. And, because the two-year statute of limitations did not begin to run until they were put on inquiry notice, their December 23, 1993 complaint was timely.
Because the Lambs filed their complaint within the two-year period, there is no reason to consider John's Heating's argument that the Lambs did not sue within a reasonable time after they discovered or should have discovered all the elements of their cause of action.[40]

C. The Lambs' Concededly Incorrect Attorney's Fees Awards Require Correction.
The superior court awarded the Lambs the attorney's fees proposed by the Lambs' counsel: $50,969.13 to Michael and $57,587.02 to Cynthia.
Although John's Heating argues that any issue about the Lambs' attorney's fees should be moot because it is entitled to a favorable judgment, it alternatively contends that correct application of Alaska Civil Rule 82 yields attorney's fees of $48,969.13 for Michael and $55,587.02 for Cynthia, rather than the amounts the court awarded. The Lambs' lawyer concedes that she erroneously calculated the fees under Rule 82, and agrees with the corrections proposed by John's Heating.
We therefore remand for the corrections John's Heating proposes. Michael is entitled to an attorney's fees award of $48,969.13 and Cynthia is entitled to an attorney's fees award of $55,587.02.[41]

IV. CONCLUSION
For these reasons, we REMAND for correction of the attorney's fees awards, but otherwise AFFIRM the judgment below.
NOTES
[1]  John's Heating Serv. v. Lamb, 46 P.3d 1024, 1033 (Alaska 2002) (John's Heating I).
[2]  Id. In an earlier case, Brigdon v. Lamb, 929 P.2d 1274 (Alaska 1997), we considered the Lambs' claims against the owners of the house in which the Lambs lived.
[3]  John's Heating I, 46 P.3d at 1028.
[4]  Id.
[5]  Id.
[6]  Id. at 1029.
[7]  Id.
[8]  Id.
[9]  John's Heating I, 46 P.3d at 1029.
[10]  Id.
[11]  Id. at 1028.
[12]  Id. at 1029.
[13]  Id. at 1028.
[14]  Id. at 1033, 1044.
[15]  John's Heating I, 46 P.3d at 1031 n. 21. A person is on "inquiry notice" when she "has sufficient information to prompt an inquiry into the cause of action, if all the elements of the cause of action may reasonably be discovered within the statutory period when a reasonable time remains within which to file suit." Cameron v. State, 822 P.2d 1362, 1365 (Alaska 1991). A person on inquiry notice is "deemed to have notice of all facts which reasonable inquiry would disclose." Id. (quoting Mine Safety Appliances Co. v. Stiles, 756 P.2d 288, 292 (Alaska 1988)).
[16]  Peterson v. Ek, 93 P.3d 458, 463 (Alaska 2004).
[17]  Id. (quoting Demoski v. New, 737 P.2d 780, 784 (Alaska 1987)).
[18]  Rausch v. Devine, 80 P.3d 733, 737 (Alaska 2003).
[19]  Alaska Travel Specialists, Inc. v. First Nat'l Bank of Anchorage, 919 P.2d 759, 762 (Alaska 1996); State, Dep't of Corr. v. Welch, 805 P.2d 979, 982 (Alaska 1991) (holding that if facts are uncontroverted, the question whether a reasonable person was on inquiry notice can be resolved as matter of law) (citing Mine Safety Appliances, 756 P.2d at 292).
[20]  AS 09.10.070(a) states that "[e]xcept as otherwise provided by law, a person may not bring an action . . . for personal injury or death . . . unless the action is commenced within two years of the accrual of the cause of action."
[21]  The superior court stated: "The Lambs were on inquiry notice more than two years before suit was filed in December 1993."
[22]  Cameron v. State, 822 P.2d 1362 (Alaska 1991).
[23]  John's Heating Serv. v. Lamb, 46 P.3d 1024 (Alaska 2002) (John's Heating I).
[24]  Cameron, 822 P.2d at 1366; see also John's Heating I, 46 P.3d at 1031. We also explained the rule in Pedersen v. Zielski, 822 P.2d 903, 908 (Alaska 1991), a case in which the plaintiff's inquiry was not successful until after the two-year statute of limitations had run.
[25]  Cameron, 822 P.2d at 1367.
[26]  John's Heating I, 46 P.3d at 1031-32 (emphasis added) (quoting Cameron, 822 P.2d at 1367).
[27]  Id. at 1033. Summary judgment is not appropriate unless the party is entitled to judgment as a matter of law and unless there is no genuine issue of material fact. Palmer v. Borg-Warner Corp., 818 P.2d 632, 634 (Alaska 1990).
[28]  John's Heating I, 46 P.3d at 1033.
[29]  Id. If the Lambs were put on inquiry notice on or after December 22, 1991, their December 23, 1993 personal injury complaint unquestionably satisfied the applicable two-year statute of limitations.
[30]  John's Heating I, 46 P.3d at 1033.
[31]  Id.
[32]  Id.
[33]  See id. at 1031.
[34]  See Cameron, 822 P.2d at 1366.
[35]  John's Heating I, 46 P.3d at 1031.
[36]  Dawson v. Temanson, 107 P.3d 892, 896 (Alaska 2005) (holding that appellees can properly argue alternative bases for trial court decision even if they did not cross-appeal).
[37]  John's Heating I, 46 P.3d at 1033.
[38]  If a reasonable inquiry is unsuccessful in revealing the elements at a point when there remains a "reasonable time" in which to sue, "the limitations period is tolled until a reasonable person discovers actual knowledge of, or would again be prompted to inquire into, the cause of action." Id. at 1031-32 (quoting Cameron, 822 P.2d at 1367).
[39]  See Part II. The superior court found that the Lambs made a reasonable inquiry that was not successful until January 1993. It also found that it was "not reasonable to expect the Lambs" to discover the causal relationship between their "old and sooty furnace" and their "mysterious symptoms" and that they were unable to discover this relationship despite a reasonable inquiry. The court also appears to have found that the Lambs did not have actual knowledge earlier than the spring of 1993, that they might have suffered brain damage or that there might be a connection between their symptoms and exposure to carbon monoxide. John's Heating does not dispute these findings. Nor does it contend that the Lambs' inquiries before January 31, 1993 were unreasonable.
[40]  John's Heating also asserts that the superior court committed legal error in giving the Lambs two full years in which to file suit after their inquiry became successful in January 1993. This claim of error presupposes that the Lambs were on inquiry notice for more than two years before they filed suit. Our holding that they were not makes it unnecessary to consider this claim of error.
[41]  John's Heating also argues that some documents contained in the Lambs' excerpts of record were not admitted into evidence and that the Lambs did not appeal from their exclusion. We need not reach this argument, because we have not relied on those documents in resolving this appeal.
