
570 F.3d 758 (2009)
UNITED STATES of America, Plaintiff-Appellee,
v.
Anthony V. LAPSINS, Defendant-Appellant.
No. 07-4387.
United States Court of Appeals, Sixth Circuit.
Argued: April 21, 2009.
Decided and Filed: July 7, 2009.
*761 ARGUED: H. Louis Sirkin, Sirkin Pinales & Schwartz LLP, Cincinnati, Ohio, for Appellant. Christy L. Muncy, Assistant United States Attorney, Cincinnati, Ohio, for Appellee. ON BRIEF: H. Louis Sirkin, Scott Ryan Nazzarine, Sirkin Pinales & Schwartz LLP, Cincinnati, Ohio, for Appellant. Christy L. Muncy, Assistant United States Attorney, Cincinnati, Ohio, for Appellee.
Before: BATCHELDER and COLE, Circuit Judges; LAWSON, District Judge.[*]

OPINION
COLE, Circuit Judge.
Anthony Lapsins was indicted on three counts related to the possession and transportation of child pornography. Following the denial of his motion to suppress evidence obtained through a warranted search of his home, he pleaded guilty to one count of transporting and shipping child pornography in violation of 18 U.S.C. § 2252(a)(1), conditional upon his right to appeal the suppression ruling. On appeal, he claims that the search warrant was not supported by probable cause. He also argues that he was erroneously denied a three-pointas opposed to a two-point reduction for acceptance of responsibility in his criminal offense level under § 3E1.1 of the United States Sentencing Guidelines (the "Guidelines" or "U.S.S.G.") and challenges the procedural and substantive reasonableness of his sentence. For the following reasons, we AFFIRM the district court's denial of the suppression motion and AFFIRM Lapsins's sentence.

I. BACKGROUND
The following facts were set forth in the affidavit of Federal Bureau of Investigation Special Agent Jeffrey Klain, which was submitted to a federal magistrate judge in support of Klain's request for a warrant to search Lapsins's house.
Lapsins came to the attention of law enforcement officials in Ohio through a separate investigation of a suspected child pornographer in Greensburg, Pennsylvania (the "Greensburg Suspect"). On October 27, 2005, Greensburg police officer Robert Jones ("Patrolman Jones" or "Jones"), working as part of a Pennsylvania State Police Computer Crime Task Force, was examining the hard-drive of the Greensburg Suspect's computer and discovered a transcript of a "Yahoo! Instant Messenger" conversation (the "chat"), dated March 27, 2005, between the Greensburg Suspect and a then-unknown person using the screen-name "budmanoh69." In the chat, budmanoh69 made the following statements:
"its so hot to see a young little girls undeveloped body."
"when I see a very young hot little girl alone i cant stop from trying to expose *762 my cock to her or try to fondle or molest her."
In response to the question, "have you had a little one," budmanoh69 replied, "ooohhh yes."
"i let a guy i met online molest my daughter at 8mos ... it was extremely hot" [this was not true, as budmanoh69later discovered to be Lapsins does not have a daughter].
"you have any hot xxx baby pics? ... want one that we can look at and talk about on the phone? ? ... you get it?... sent."
"we going to look at that pic on the phone together? ?"
(Record on Appeal ("ROA") 73-74.) During the chat, budmanoh69 provided the Greensburg Suspect with a phone number so they could discuss the image budmanoh69 had sent.
Patrolman Jones also located an email that budmanoh69 sent to the Greensburg Suspect during the course of the chat from the email address budmanoh69@aol.com. Attached to the email was an image that "depict[ed] a baby girl with an erect adult penis in the foreground and ejaculate covering the exposed vaginal area of the baby girl." (ROA 75.) Patrolman Jones sent the image to the National Center for Missing and Exploited Children ("NCMEC"), a "national clearinghouse that gathers information about missing and sexually exploited children for law enforcement use." (ROA 59-60.) According to Jones, as set forth in Special Agent Klain's affidavit, the NCMEC "concluded that [the image] was a known victim image from the Camille [photograph] series, identifiable by Yves Goethals of the Belgian National Police." (ROA 76.)
On November 3, 2005, Patrolman Jones sent America On-Line ("AOL") a court order directing it to provide him with subscriber and billing information for the individual using the AOL email address "budmanoh69@aol.com." AOL informed Jones that the email account was registered to Anthony Lapsins, who had provided as his address 8065 Kingfisher Lane in West Chester, Ohio. Several AOL screen-names were associated with the budmanoh 69@aol.com email address, including budmanoh69, tonylapl, cincym, carmen4fun, and lapsins. AOL also provided Jones with a telephone number for Lapsinsthe same number budmanoh69 had given the Greensburg Suspect. Jones also obtained a court order requiring Yahoo! to provide information about the user of the Yahoo! screen-name budmanoh69 and learned that the user of that screen-name had listed budmanoh69@aol.com as an alternate email address.
Patrolman Jones requested from the NCMEC any "CyberTipline Reports" concerning budmanoh69. According to Klain's affidavit, "CyberTipline Reports" are "reports forwarded from NCMEC to the law enforcement community ... based on information obtained from various sources to include individuals and members of the Internet services industry." (ROA 60.) The NCMEC "neither investigates nor vouches for the accuracy of the information reported to itself [and] forwards all information unedited to law enforcement agencies for investigation and disposition pursuant to its congressional mandate to operate as a clearinghouse." (ROA 60.) Jones received a CyberTipline report stating that, on November 14, 2005, budmanoh69, using IP address 71.64.193.15, uploaded 132 child pornographic images to the website http:// photos.yahoo.com/budmanoh69. The report stated that the IP address was assigned to a server designated "cinci.res.rr.com." Special Agent Klain contacted Time Warner Cable and learned that this server provides residential cable modem service in the Cincinnati area, which "can only be *763 used where the cable modem is installed." (ROA 78.)
A West Chester police officer working with Klain contacted Cincinnati Bell and confirmed that the telephone number Lapsins had given the Greensburg Suspect was a Cincinnati Bell Wireless cellular phone number registered to Anthony Lapsins at the Kingfisher Lane address. Klain confirmed, via Ohio Bureau of Motor Vehicles records, West Chester Police Department records, and Butler County property records, that Lapsins lived at the Kingfisher Lane address.
Based on the above information, a magistrate judge granted Klain a search warrant for Lapsins's house on December 19, 2005. The warrant was executed the following day, and investigators seized Lapsins's computer, various computer-related equipment, and numerous compact discs, Zip disks, and other diskettes. According to the Presentence Investigation Report ("PSR"), these materials contained approximately 1400 images of child pornography, including the image that had been emailed to the Greensburg Suspect, and sixty-nine pornographic videos of children. Also according to the PSR, Lapsins admitted to investigating agents that he sent the image to the Greensburg Suspect, possessed child pornography, and created a Yahoo! group to share child pornography.
The district court found that the warrant to search Lapsins's house was supported by probable cause and denied his motion to suppress the evidence obtained from the search. Lapsins entered a conditional guilty plea and was sentenced to 168 months in prison, followed by supervised release for life.

II. ANALYSIS

A. Suppression motion
Lapsins argues that the warrant authorizing the search of his house was not supported by probable cause. He contends that Klain's supporting affidavit did not provide reason to believe that the pornographic images at issue were photographs of real children, as opposed to computer-generated images, or that evidence related to the suspected crime would be located at Lapsins's house. He also argues that the information on which the warrant relied was stale because one of the major events described in the affidavit, the Yahoo! chat and emailing of the image to the Greensburg Suspect, occurred nine months before the warrant was issued.

1. Standard of review and probable cause standard
In an appeal following the denial of a motion to suppress evidence, we review the district court's factual findings for clear error and its legal conclusions de novo. See United States v. Terry, 522 F.3d 645, 647 (6th Cir.2008). "[W]hen judging the sufficiency of an affidavit to establish probable cause in support of a search warrant, the Supreme Court has `repeatedly said that after-the-fact scrutiny... should not take the form of de novo review.... Rather, reviewing courts are to accord the magistrate's determination `great deference.''" Id. (quoting United States v. Allen, 211 F.3d 970, 973 (6th Cir.2000) (en banc) (quoting Illinois v. Gates, 462 U.S. 213, 236, 103 S.Ct. 2317, 76 L.Ed.2d 527 (1983))). "`[S]o long as the magistrate had a `substantial basis for ... concluding' that a search would uncover evidence of wrongdoing, the Fourth Amendment requires no more.'" Allen, 211 F.3d at 973 (quoting Gates, 462 U.S. at 236, 103 S.Ct. 2317 (quoting Jones v. United States, 362 U.S. 257, 271, 80 S.Ct. 725, 4 L.Ed.2d 697 (1960))).
"In deciding whether to issue a search warrant, the Fourth Amendment requires `the issuing magistrate ... simply to make a practical, common-sense decision *764 whether, given all the circumstances set forth in the affidavit before him ... there is a fair probability that contraband or evidence of a crime will be found in a particular place.'" Terry, 522 F.3d at 648 (quoting Gates, 462 U.S. at 238, 103 S.Ct. 2317). "[P]robable cause requires only a probability or substantial chance of criminal activity, not an actual showing of such activity." Gates, 462 U.S. at 243 n. 13, 103 S.Ct. 2317.

2. The affidavit provided probable cause to believe that Lapsins possessed pornographic images of real children, rather than solely computer-generated images
Lapsins argues that there was insufficient evidence that the images referenced in the affidavit were images of actual children as opposed to computer-generated images, which are not unlawful to possess. See Ashcroft v. Free Speech Coalition, 535 U.S. 234, 256, 122 S.Ct. 1389, 152 L.Ed.2d 403 (2002) (holding that Congress's ban on possession of virtual child pornography violated the First Amendment because, among other reasons, its creation does not involve actual children). This argument fails because the affidavit contained several assertions that, considered together and under the totality of the circumstances, provided probable cause to believe that the pornographic images at issue included images of real children. See Gates, 462 U.S. at 238, 103 S.Ct. 2317 (holding that a totality-of-the-circumstances analysis applies to probable-cause determinations).
The affidavit stated that the child in the image emailed by Lapsins was a known victim who, according to the NCMEC, was identifiable by Yves Goethals, a Belgian police officer. While Lapsins is correct that the affidavit provided no additional information about Goethals's reliability, in general, "another law enforcement officer is a reliable source and ... consequently no special showing of reliability need be made as a part of the probable cause determination." 2 Wayne R. LaFave, Search and Seizure § 3.5(a) (4th ed.2008). On the other hand, Klain learned of this information indirectly through an NCMEC report, and "long chains of information passed through police channels" are deemed less reliable, particularly when the affidavit does not set forth the factual basis for an officer's statement. Id. We need not arrive at an exact measure of Goethals's reliabilitythe fact that a law enforcement officer claimed to have identified the child in the photograph, when combined with the other information presented in the affidavit, provided sufficient probable cause to believe that Lapsins possessed images of real children.
The affidavit also stated that the "NCMEC analyzed the image [emailed to the Greensburg Suspect] and concluded that [it depicted] a known victim." (ROA 76.) While the NCMEC's conclusion as to the identifiability of the victim was based on information provided by Goethals, the affidavit also stated that the NCMEC, which has expertise in child pornography, "analyzed" the image and informed Patrolman Jones that it was a photograph of an identified victim, i.e., a real child. The magistrate judge could reasonably have assumed that the NCMEC would not have made such an assertion if the image had appeared to be a virtual, computer-generated image.
In addition, the affidavit shows that Patrolman Jones viewed the image emailed to the Greensburg Suspect, and although the affidavit does not contain a statement by Jones that he believed the photograph to depict a real child, the affidavit as a whole implies such a belief. According to the affidavit, "Patrolman Jones's forensics show that the image sent in the body of the email ... depict[ed] a baby girl with *765 an erect adult penis in the foreground and ejaculate covering the exposed vaginal area of the baby girl." (ROA 75.) Jones, who was trained in computer forensics and the investigation of child pornography, provided Agent Klain with the NCMEC's conclusion that the image depicted a known child-victim. The overall implication is that Jones did not believe that the image was computer-generated (such that it could not possibly depict a real child), and this contributed to the reasonableness of the magistrate's common-sense conclusion that the image Lapsins sent likely depicted a real child.
In addition to information suggesting that the image emailed to the Greensburg Suspect was a photograph of a real child, the warrant relied on a report by Yahoo! to the NCMEC stating that Lapsins uploaded 132 images of child pornography to the budmanoh69 site on a specified date. While the affidavit did not contain descriptions of the images, nor an assertion that any of the photographs depicted real children rather than computer-generated images, at the probable-cause stage of the analysis, the magistrate judge would have been justified in finding that Lapsins's possession of such a large quantity of purported child pornography contributed to the "fair probability" that some of the images Lapsins possessed were of real children, though we express no opinion about whether such a report, on its own, would support a finding of probable cause. Although we find that the affidavit was sufficient on this point in the present case, the better practice would be to include a plain statement of the affiant's belief that the image depicted a real child, together with a recitation of the facts that support such belief.
Neither at the suppression hearing nor on appeal has Lapsins pointed to any information that would have suggested to the investigating officers or the magistrate that the images were not of real children. Although the burden of demonstrating probable cause rests with the Government, we have held that "[s]ince a probable cause finding does not require a preponderance of the evidence, in order to undermine the magistrate's finding, the likelihood of an innocent explanation must (at the very least) be greater than the likelihood of a guilty one." Terry, 522 F.3d at 650 (holding that the possibility that a pornographic image emailed by defendant was an innocent reply to a spam message to which the image had been attached by the original sender did not negate finding of probable cause). Nothing in Lapsins's chat with the Greensburg Suspect, for example, provided any reason to believe that Lapsins was referring something other than a photograph of a child when he offered to send a "hot xxx baby pic []" shortly after describing his urge to molest real children.
As required at the probable-cause stage, the warrant in this case was supported by "a probability or substantial chance of" possession of images of actual children; "an actual showing" that the images depicted real children was not required, see Gates, 462 U.S. at 243 n. 13, 103 S.Ct. 2317, even though such a showing was arguably made through the information provided by Goethals. See also United States v. Wagers, 452 F.3d 534, 538-39 (6th Cir.2006) (holding that defendant's subscriptions to websites containing child pornography but also possibly containing adult pornographic images provided probable cause for a search warrant even though the supporting affidavits did not specifically allege that the defendant had viewed the child pornography on the sites). In this case, the magistrate judge permissibly found a "fair probability" that some of the images in Lapsins's possession were images of real children.


*766 3. The affidavit set forth a sufficient nexus between the suspected illegal activity and Lapsins's home

Lapsins argues that even if the affidavit established probable cause to believe that he had transmitted images of child pornography over the internet, it did not provide probable cause that such images would be found in his home. While Lapsins is correct that the mere fact that a person is suspected of a crime does not justify the conclusion that fruits of that crime will be found at his residence, see United States v. McPhearson, 469 F.3d 518, 524-25 (6th Cir.2006) (holding that suspect's possession of drugs on his person did not provide probable cause to search his home), in this case, the affidavit included information providing a sufficient nexus to Lapsins's home.
As an initial matter, Lapsins does not dispute that ample evidence connected him to the budmanoh69 Yahoo! and AOL screen-names and email address, and established that he lived at the Kingfisher Lane address. Despite Lapsins's arguments to the contrary, the affidavit also set forth evidence giving rise to a fair probability that images of child pornography transmitted by budmanoh69 would be found in Lapsins's home, particularly on a home computer. The pictures uploaded by budmanoh69 to the budmanoh69 Yahoo! group on November 14, 2005 originated from an IP address associated with a residential cable modem in the Cincinnati area. See Terry, 522 F.3d at 648 (concluding that where suspect was registered user of AOL account from which image was sent at 2:30 a.m. and was known to have a home computer through which he accessed that account, it "requires no great leap of logic" to conclude that his home computer was probably used to send the image). Lapsins's chat with the Greensburg Suspect took place between the hours of 6:30 and 8:30 in the morninga time when Lapsins likely would have been using a home computer. See id. at 649 n. 1. Furthermore, his upload of 132 images to the budmanoh69 Yahoo! site was traced to a residential cable modem server in the Cincinnati area. In addition, this particular "criminal activity (viewing child pornography) is much more tied to a place of privacy, seclusion, and high-speed Internet connectivity (e.g. a home or office) than the storing of drugs." Wagers, 452 F.3d at 540; see also Terry, 522 F.3d at 648 ("[T]he district court did not err in concluding that as a matter of plain common sense, if ... a pornographic image has originated or emanated from a particular individual's email account, it logically follows that the image is likely to be found on that individual's computer or on storage media associated with the computer." (internal quotation marks omitted)).
Although the affidavit did not allege that the IP address from which budmanoh69 uploaded child pornography was registered to Lapsins by name, cf. Wagers, 452 F.3d at 539 (IP address specifically assigned to defendant was used to purchase website subscriptions), we stated in Terry that "the Wagers opinion did not hold that IP information was an indispensable prerequisite to obtaining a search warrant ..., only that such information contributed to the totality of the probable cause determination." Terry, 522 F.3d at 649. In this case, as in Terry, there was also evidence that the defendant had actually possessed child pornography (since he had emailed an image), as opposed to merely having had access to it, as in Wagers. The Terry court found that "use of Terry's personal e-mail account in the wee hours of the morning [to send child pornography], combined with information that Terry used his home computer to access that account, established at least a `fair probability' that the computer used to send the messages was, in fact, the one in Terry's home." Id. *767 Here, there was no direct evidence that Lapsins used a home computer to access his AOL or Yahoo! accounts, but the fact that images were uploaded by budmanoh69 from a residential cable modem in the city where Lapsins lived, combined with the early morning chat, allowed the magistrate judge to make that inference.
Lapsins claims that the report from the NCMEC that he had uploaded 132 images on a certain date is unreliable because the NCMEC relies on information from "various sources [ ] includ[ing] individuals and members of the Internet services industry," and "neither investigates nor vouches for the accuracy of the information reported to itself." (ROA 60.) According to the affidavit, the NCMEC informed Patrolman Jones of "past reports by Yahoo! of budmanoh69 uploading child pornography to Yahoo! groups." (ROA 77.) Jones provided Klain with these reports, one of which contained the precise date, time, and originating IP address of the upload of 132 images, as well as the screen-name of the uploader: budmanoh69. Even if the report was unreliable in isolation, it was corroborated by the fact that the upload came from a residential cable modem in the Cincinnati area and that the Yahoo! user budmanoh69 was independently known to be a transmitter of child pornography (by virtue of the email to the Greensburg Suspect). For the foregoing reasons, the warrant was supported by probable cause to believe that child pornography would be found at Lapsins's home.

4. The information supporting the warrant was not stale
The email from Lapsins to the Greensburg Suspect was sent on March 27, 2005, but the warrant application was not submitted until December 19, 2005 nearly nine months later. However, the warrant was also supported by the NCMEC report that budmanoh69 had uploaded 132 images of child pornography on November 14, 2005only about one month before the warrant was executed. Since this information was reliable enough to contribute to a finding of probable cause, it remedied any potential staleness defect. See, e.g., United States v. Prideaux-Wentz, 543 F.3d 954, 958 (7th Cir.2008) (recognizing that, in child pornography context, "more recent evidence of continuing criminal activity [can] bolster probable cause and freshen the older information"); see also Terry, 522 F.3d at 650 n. 2 (noting that pornographic images can often be recovered from computers by forensic examiners such that the passage of time does not greatly affect the probable cause calculus).

B. Sentencing Guidelines reduction for acceptance of responsibility
Lapsins argues that he was entitled to a three-point reduction in his base offense level for acceptance of responsibility, instead of the two-point reduction he received. For the following reasons, the prosecution was not required to move for the additional one-point reduction.

1. The Guideline provision
Section 3E1.1 of the Guidelines provides for a potential reduction of three points for acceptance of responsibility. Section 3E1.1(a) allows the district court to reduce the offense level by two points if "the defendant clearly demonstrates acceptance of responsibility for his offense." U.S.S.G. § 3E1.1(a). Section 3E1.1(b), on the other hand, allows for a reduction of one additional point
upon motion of the government stating that the defendant has assisted authorities in the investigation or prosecution of his own misconduct by timely notifying authorities of his intention to enter a plea of guilty, thereby permitting the *768 government to avoid preparing for trial and permitting the government and the court to allocate their resources efficiently.
U.S.S.G. § 3E1.1(b). This additional one-point reduction is not available absent a motion from the government. United States v. Smith, 429 F.3d 620, 628 (6th Cir.2005).

2. Prosecution's refusal to move for a third point
The initial PSR, dated February 7, 2007, recommended that Lapsins receive a full three-point reduction for acceptance of responsibility, finding that a letter he had submitted to the court revealed that he had accepted responsibility and that his decision to plead guilty had permitted the government to avoid preparing for trial.
In a March 2, 2007 memorandum to the United States Probation Office ("USPO"), Lapsins lodged a number of objections to the description of his offense contained in the initial PSR. In particular, Lapsins denied that he had created a Yahoo! "group," attempting to distinguish a Yahoo! "photos" website from a Yahoo! "groups" website. He also stated that he "denies ever having had a Yahoo group, and the government has presented no evidence of such," and that he "emphatically denies ever having started a child pornography Yahoo group." (Docs. Under Seal 51-52.[1]) He also objected to a statement in the PSR that he owned and controlled the membership of a Yahoo! group. The Government argued that these statements directly contradicted Lapsins's prior sworn admission in the "Statement of Facts" attached to his plea agreement that he "had created the Yahoo Group `budmanoh69,'" which "facilitated the distribution and sharing of child pornography." (ROA 178.)
In his memorandum to the USPO, Lapsins also denied the statement in the PSR that he uploaded 132 images to the budmanoh69 Yahoo! group on November 14, 2005, claiming that his screen-name had been stolen. Lapsins also objected to the PSR's statement about the number of photographs and videos he had possessed and uploaded to the budmanoh69 site, arguing that "[b]ecause there is no proof or substantiation of these allegations, they should be stricken from the record." (Docs. Under Seal 52.)
As a result of these objections, the USPO, in a revised PSR dated March 23, 2007, changed its position and recommended that Lapsins not receive any reduction for acceptance of responsibility because, although he had "made a statement detailing his involvement in the instant offense," he "later denied portions of the Statement of Facts." (Docs. Under Seal 34.)
At an evidentiary hearing to address Lapsins's objections to the initial PSR, the prosecutor argued that "[Lapsins] is either lying then or he's lying now and he's subject to a perjury prosecution, and it would be inappropriate for this Court to grant him acceptance of responsibility having previously stated under oath that the Statement of Facts is accurate yet stand[ing] here today denying [it]." (ROA II,[2] Sept. 26, 2007 Evid. Hr'g 21.) The prosecutor also stated, "if I were in [defense *769 counsel's] shoes, Your Honor, I would simply withdraw the objection.... Then there is no possibility of there being anything contrary.... Whether he distributed 132 images on a particular day or 400 on another day doesn't affect the Guidelines." (Id. 21-22.) In response to this argument, Lapsins's counsel withdrew the objections.
At sentencing, the Government urged the district court not to award any reduction for acceptance of responsibility, claiming that Lapsins's objections to the initial PSR, as well as a sentencing memorandum he filed just prior to sentencing that used the word "allegedly" to describe acts to which Lapsins had pleaded guilty, showed that he had not accepted responsibility. In addition, the prosecutor stated: "Clearly, the [G]overnment is not going to give that third point [under § 3E1.1(b)]." (ROA II, Sent'g Hr'g 6.) The prosecutor argued that he was entitled to refuse to move for a reduction because the plea agreement stated that if Lapsins made false statements or misrepresentations to any government entity following his plea, the Government would not be obligated to make certain recommendations in his favor, including moving for a one-point reduction under § 3E1.1(b).
The district judge was not persuaded by the prosecutor or the USPO, and he determined that Lapsins's Statement of Facts and guilty plea merited a two-level reduction under § 3E1.1(a). At sentencing, the district judge made no comment about the Government's decision not to move for an additional one-point reduction. The judge went on to calculate a Guidelines range of 168 to 210 months, and sentenced Lapsins to 168 months' imprisonment. (If the Government had moved for the additional one-point reduction, the recommended range would have been 151 to 188 months.)

3. The prosecutor was not required to move for the additional reduction
The Government urges that we should review for plain error the district court's failure to require the prosecution to move for the additional point, claiming that Lapsins's counsel did not specifically object to the Government's decision not to move for the additional point. Lapsins points out that he had already argued several times, including during the sentencing hearing, that his objections to the PSR did not indicate an unwillingness to accept responsibility. We need not resolve this question because Lapsins's argument fails even under a de novo standard of review.
U.S.S.G. § 3E1.1(b) commits the decision whether to file a motion for an additional one-point reduction to the government's discretion, and we have held that this discretion is subject to the limitation that the government may not act with a constitutionally impermissible motive. See Smith, 429 F.3d at 628 (citing Wade v. United States, 504 U.S. 181, 186-87, 112 S.Ct. 1840, 118 L.Ed.2d 524 (1992) (holding that prosecutor's decision not to move for a sentence reduction for substantial assistance must bear a rational relation to legitimate government end and must not be based on factors such as religion, sex, or race)); see also United States v. Drennon, 516 F.3d 160, 162-63 (3d Cir.2008) (holding that the prosecutor's decision not to move for a § 3E1.1(b) reduction is entitled to "full deference" unless the record shows the decision was attributable to an unconstitutional motive); United States v. Espinoza-Cano, 456 F.3d 1126, 1138 (9th Cir. 2006) (defendant must present objective evidence of an improper motive or arbitrary action to overcome government's decision not to move for reduction under U.S.S.G. § 3E1.1(b)).
This case differs from the typical case involving § 3E1.1(b) because the government's *770 decision to move for the reduction is usually based on whether the defendant pleaded guilty early enough to save the government the expense of preparing for trial. See, e.g., Smith, 429 F.3d at 628 (explaining that the government is given the discretion to move for the reduction or not because it is in the best position to know whether the defendant's cooperation and acceptance of responsibility have allowed the government to preserve resources); see also U.S.S.G. § 3E1.1 cmt. n.6 (same). Although the Government argues in its brief that Lapsins did not save it the resources he might have, it is apparent that the real reason the Government refused to move for the reduction was that "the defendant made objections to the initial PSR that were contradictory to statements he had sworn to in the signed Statement of Facts. Because of this less than candid position, the government felt the defendant was no longer deserving of acceptance of responsibility." (Gov't Br. 39.) The record makes clear that the prosecutor did not believe that Lapsins had fully accepted responsibility for his actions. (See, e.g., ROA II, Sent'g Hr'g 23 ("[H]e continues to use the word `allegedly.' This is an individual who still can't wrap his brain around his conduct.... It's not allegedly anymore. Come on. Just admit it, once.").)
Section 3E1.1(b) does not state that the prosecutor can refuse to move for the reduction because he does not agree with the district court's determination that the defendant has accepted responsibility, and the text of the provision focuses on whether the defendant has allowed the government to avoid preparing for trial. This might suggest that the government is required to base its decision about whether to move for the reduction solely on whether the defendant has saved the government resources. However, the Second Circuit recently addressed this issue and held that the government is entitled to refuse to move for the reduction based on its belief that the defendant has not genuinely accepted responsibility, even if the district court awards a two-point reduction under § 3E1.1(a). See United States v. Sloley, 464 F.3d 355, 359 (2d Cir.2006). The Second Circuit found that to hold otherwise would be to ignore both the plain language of § 3E1.1(b), which allows for the reduction "upon motion of the government," and comment 6 to that section, which states that "an adjustment under subsection (b) may only be granted upon formal motion by the government." U.S.S.G. § 3E1.1(b) & cmt. 6; Sloley, 464 F.3d at 359. The Sloley court also reasoned that subsection (b) would be rendered a nullity if the government were required to agree with the court's assessment of acceptance of responsibility: "Section 3E1.1 is crafted and structured in a manner that divides the power to reduce a defendant's offense level for acceptance of responsibility between the sentencing court and the prosecutor. Such a division of power ... implicitly contemplates situations in which a court may find acceptance of responsibility while the government prosecutor may not." Sloley, 464 F.3d at 359. We find the Second Circuit's reasoning persuasive. While on its face § 3E1.1(b) does not appear to contemplate the prosecutor's refusal to move for the point for any reason other than the wasting of government resources, to hold that the district court could compel the government to make the motion would be directly contrary to the section's commitment of this decision to the government's discretion.
Therefore, we conclude that the government may decline to move for a reduction under § 3E1.1(b) so long as the decision does not rest on a constitutionally impermissible factor and is not arbitrary. See Wade, 504 U.S. at 186-86, 112 S.Ct. *771 1840; Smith, 429 F.3d at 628. We do not reach the situation in which the prosecutor has promised, as a condition of the defendant's guilty plea, to move for the reduction because Lapsins's counsel conceded at oral argument that no such promise was made in this case. As Lapsins does not allege that the Government acted based on a constitutionally impermissible factor, the question remaining is whether the Government's decision not to move for the reduction was arbitrary.
Lapsins essentially argues that the prosecutor's decision was arbitrary because there was no valid reason for him to conclude that Lapsins had not accepted responsibility. On the contrary, Lapsins claims, the record shows that he was truly remorseful for his crimes, and the prosecutor misinterpreted defense counsel's use of the word "allegedly" and filing of various factual objections to the PSR as manifesting Lapsins's refusal to accept responsibility, when in fact they merely represented legal strategy by defense counsel. While it is true that Lapsins's counsel withdrew the objections to the PSR (under pressure from the prosecutor), and while the use of "allegedly" may not be a good indicator of Lapsins's own mindset, the record nonetheless shows that Lapsins attempted to retract his admission to forming a Yahoo! group devoted to child pornography. For example, at the September 26, 2007 evidentiary hearing (which post-dated Lapsins's sworn admissions in the Statement of Facts) after conferring with Lapsins, defense counsel stated to the district judge, "He is claiming he did not create the group." (See ROA II, Sept. 26, 2007 Evid. Hr'g 19); cf. Sloley, 464 F.3d at 361 ("[T]he record shows that Sloley's reneging on his admission ... made in the plea agreement ... is what led the government to conclude that he had not accepted responsibility."). Given that Lapsins denied his prior sworn admissions, that § 3E1.1(b) commits the decision whether to move for the reduction to the discretion of the prosecutor, and that the record shows that the prosecutor believed in good faith that Lapsins had not accepted responsibility, we hold that the prosecutor's decision not to move for the reduction was permissible.

C. Reasonableness of sentence

1. Lapsins's claims of sentencing error
Lapsins claims his sentence was procedurally unreasonable because the district court failed to consider certain arguments relating to the factors set forth in 18 U.S.C. § 3553(a) and gave only a conclusory explanation of his sentencing decision. While Lapsins generally frames his argument as one of procedural unreasonableness, he appears to assert a substantive unreasonableness claim as well. At the outset, it is worth noting that the district judge was generous to Lapsins in several respects: he granted Lapsins a downward variance from Criminal History Category II to Category I, finding that "based upon the prior conduct of the defendant, [Criminal History Category II] overstates hisit over-represents his criminal history, and so I'm going to make a variance pursuant to [U.S.S.G. §] 4A1.3 to indicate that he has a Criminal History Level of I." (ROA II, Sent'g Hr'g 11-12.); he granted Lapsins a two-point reduction in Criminal Offense Level for acceptance of responsibility despite the USPO's recommendation to the contrary; and he sentenced Lapsins at the bottom of the recommended Guidelines range.
Lapsins claims that the court failed to consider his asserted "relatively low chance of recidivism," his "strong, dedicated support system," his "shame and guilt," his successful work history, his "willingness and desire to seek counseling," and the fact that he was battling a substance abuse problem, all of which, Lapsins *772 claims, pointed to a below-Guidelines sentence. (Lapsins Br. 44-46.) In addition, Lapsins argues that the district court failed to address his arguments that a below-Guidelines sentence would be sufficient to provide specific deterrence and that a long incarceration would interfere with his ability to seek treatment and counseling. Lapsins also argues that the district court failed to address his argument that he should receive a significant downward departure similar to that upheld on appeal by this Court in United States v. Cherry, 487 F.3d 366 (6th Cir.2007), because the circumstances of the two defendants are similar, and to refuse to give Lapsins a similar departure would result in an unwarranted sentencing discrepancy.

2. Standard of review
Following United States v. Booker, 543 U.S. 220, 125 S.Ct. 738, 160 L.Ed.2d 621 (2005), we review a district court's sentencing decisions "under a deferential abuse-of-discretion standard" for reasonableness. Gall v. United States, 552 U.S. 38, 128 S.Ct. 586, 591, 169 L.Ed.2d 445 (2007); United States v. Stephens, 549 F.3d 459, 464 (6th Cir.2008). This inquiry has both a procedural and a substantive component. Gall, 128 S.Ct. at 597.
A sentence is procedurally unreasonable if the district court failed to calculate (or improperly calculated) the Guidelines range, treated the Guidelines as mandatory, failed to consider the § 3553(a) factors, selected a sentence based on clearly erroneous facts, or failed adequately to explain the chosen sentence. Gall, 128 S.Ct. at 597. We review the district court's application of the Sentencing Guidelines de novo and its findings of fact at sentencing for clear error. See United States v. Hunt, 487 F.3d 347, 350 (6th Cir.2007).
If a sentence is procedurally sound, we then consider its substantive reasonableness. Gall, 128 S.Ct. at 597. A sentence is substantively unreasonable if the district court "selects a sentence arbitrarily, bases the sentence on impermissible factors, fails to consider relevant sentencing factors, or gives an unreasonable amount of weight to any pertinent factor." United States v. Conatser, 514 F.3d 508, 520 (6th Cir.2008). Sentences imposed within a properly-calculated Guidelines range enjoy a rebuttable presumption of substantive reasonableness on appeal. United States v. Vonner, 516 F.3d 382, 389 (6th Cir.2008) (en banc); see also Rita v. United States, 551 U.S. 338, 347, 127 S.Ct. 2456, 168 L.Ed.2d 203 (2007) ("[A] court of appeals may apply a presumption of reasonableness to a district court sentence that reflects a proper application of the Sentencing Guidelines.").
After the district judge announced Lapsins's sentence, he asked both counsel for objections, and defense counsel stated that he had no objections other than those already raised. Because Lapsins did not object to the district court's explanation of the § 3553(a) factors, we review Lapsins's challenge to the sufficiency of that explanation for plain error. See Vonner, 516 F.3d at 386. This requires Lapsins to show (1) error (2) that "was obvious or clear," (3) that "affected defendant's substantial rights," and (4) that "affected the fairness, integrity, or public reputation of the judicial proceedings." Id. (internal quotations omitted).

3. Analysis
Because the sentence was within the Guidelines range, a rebuttable presumption of reasonableness applies. See Vonner, 516 F.3d at 389. Here, although the district judge could have said more about why he chose not to accept Lapsins's arguments for a downward departure, the sentence *773 was not plainly erroneous, either procedurally or substantively.
The record reveals that the district judge considered a large quantity of information relating to Lapsins's characteristics, background, psychological state, and family circumstances. The judge reviewed numerous letters submitted by Lapsins's family and heard testimony at an evidentiary hearing from the psychologist who had been treating Lapsins since his arrest. The psychologist's testimony included, at the district judge's instigation, discussion of Lapsins's treatability and likelihood of recidivism. The district judge also heard live statements from three of Lapsins's family members. The judge obviously considered Lapsins's criminal background, as he granted Lapsins a downward variance based on that background.
Lapsins concedes that the district judge was well informed about Lapsins's relevant characteristics but argues that the record must reflect both that the district judge considered the defendant's argument and that the judge explained the basis for rejecting it. The district judge's recitation of the § 3553 factors was fairly terse:
It's my duty to sentence Mr. Lapsins at this time. 18 U.S.C. [§] 3553 instructs the Court to impose a sentence which is sufficient but not greater than necessary to comply with the purposes set forth in Paragraph 2 of the section.
The Court finds that the sentence I'm about to impose is in accordance with 18 U.S.C. [§] 3553(a), as well as the proper application of the sentencing guidelines as described in 18 U.S.C. [§] 3553(a) which include:
The nature and circumstances of the offense and the history and the characteristics of Mr. Lapsins;
The sentence will also reflect the seriousness of the offense, promote respect for the law, and provide just punishment for the offense;
To afford adequate deterrence to criminal conduct;
The sentence will also protect the public from further crimes of Mr. Lapsins and, hopefully, Mr. Lapsins can get the needed educational and medical care and treatment that is needed in the most effective manner.
. . .
Therefore, Mr. Lapsins is committed to the custody of the United States Bureau of Prisons for a term of 168 months. He is ordered placed on Supervised Release for life due to the seriousness of the offense, the length of time that he was involved with the possession of child pornography, and the need for continued mental health treatment.
. . .
The court considers the sentence to be just and reasonable in light of the defendant's conduct and the applicable sentencing factors.
(ROA II, Sent'g Hr'g 25-31.)
Although the district judge did not articulate his reasons for rejecting Lapsins's arguments, his reasoning was "sufficiently detailed to reflect the considerations listed in § 3553(a) and to allow for meaningful appellate review." United States v. Mayberry, 540 F.3d 506, 518 (6th Cir.2008) (internal quotations omitted). The district court is not required to "give the reasons for rejecting any and all arguments [made] by the parties for alternative sentences." Vonner, 516 F.3d at 387. It is sufficient if the district judge "set[s] forth enough to satisfy the appellate court that he has considered the parties' arguments and has a reasoned basis for exercising his own legal decisionmaking authority." Rita, 551 U.S. at 356, 127 S.Ct. 2456; see also United States v. *774 Moon, 513 F.3d 527, 539 (6th Cir.2008) (stating that the district court must "provide some indication that the court considered the defendant's arguments in favor of a lower sentence and the basis for rejecting such arguments"); United States v. Gale, 468 F.3d 929, 940 (6th Cir.2006) (noting that remand may be appropriate where "a defendant's argument and supporting evidence presents an arguably meritorious claim for a lesser sentence, but there is little to suggest that the district court actually considered it"). A less lengthy explanation will suffice for a within-Guidelines sentence when "the record makes clear that the sentencing judge considered the [defendant's] evidence and arguments." Rita, 551 U.S. at 359, 127 S.Ct. 2456.
Although the district court did not specifically respond to Lapsins's arguments about his remorse, family support, substance abuse problems, and willingness to undergo counseling, these matters are encompassed within § 3553(a)(1), which requires a sentencing court to consider "the history and characteristics of the defendant." The district court stated that it had accounted for the "nature and circumstances of the offense and the history and the characteristics of Mr. Lapsins," as well as a number of other § 3553(a) considerations. (ROA II, Sent'g Hr'g 25.) As noted above, the record reveals that the district judge considered Lapsins's arguments and evidence in support of a downward variance (in addition to the criminal history downward variance already given). Therefore, Lapsins has not established that his sentence was procedurally unreasonable.
Lapsins's substantive unreasonableness argument is based on essentially the same claim as his procedural unreasonableness argumentthat the district court failed to consider pertinent § 3553 factors. Because the sentence falls within the properly-calculated Guidelines range, it is entitled to a presumption of reasonableness. See Vonner, 516 F.3d at 389. Lapsins's argument that he is entitled to a below-Guidelines sentence because a defendant with similar characteristics received a downward departure in United States v. Cherry can be construed as a substantive unreasonableness argument, but it is without meritthe fact that a judge in an unrelated case found a specific individual deserving of a downward departure does not mean that the judge in this case plainly erred by sentencing Lapsins within the Guidelines after considering the nature of his crime and his personal characteristics. See, e.g., United States v. Brinda, No. 07-6357, 2009 WL 1011740, ___ Fed.Appx. ___, ___ - ___, 2009 U.S.App. LEXIS 7936, at *10-11 (6th Cir. Apr. 15, 2009) (holding that defendant in child pornography case did not rebut presumption of reasonableness by pointing to other defendants who received similar sentences for purportedly more culpable conduct). Lapsins has not rebutted the presumption of substantive reasonableness accorded to within-Guidelines sentences.

III. CONCLUSION
For the foregoing reasons, we AFFIRM the district court's denial of Lapsins's suppression motion and AFFIRM Lapsins's sentence.
NOTES
[*]  The Honorable David M. Lawson, United States District Judge for the Eastern District of Michigan, sitting by designation.
[1]  "Docs. Under Seal" refers to a document, separate from the ROA, that is listed on the appellate docket sheet as "Pre-sentence report" bearing the title "Documents Under Seal."
[2]  "ROA II" refers to a document listed on the appellate docket sheet as "Record on Appeal, Transcripts, Filed. Vol 2." This non-indexed, non-consecutively paged document contains transcripts of several proceedings, including the suppression hearing and sentencing hearing. Accordingly, citations herein to ROA II include names of specific documents and page numbers within those documents.
