GRABER, Circuit Judge:
For the third time, the United States appeals the sentence imposed upon Defendant Dorothy Menyweather’s conviction by guilty plea to one count of mail fraud, in violation of 18 U.S.C. §§ 1341 and 1346. The government objects to the district [694]*694court’s eight-level downward departure for mental and emotional condition, diminished capacity, and extraordinary family circumstances, a departure that the district court has reimposed twice after remands from this court. United States v. Meny-weather, No. 01-50438, 36 Fed.Appx. 262 (9th Cir. May 16, 2002) (unpublished disposition) (“Menyweatker I ”); United States v. Menyweather, 69 Fed.Appx. 874 (9th Cir.2003) (unpublished disposition) (“Men-yweather II ”).
While this third appeal was pending, the Supreme Court decided United, States v. Booker, 543 U.S. 220, 125 S.Ct. 738, 160 L.Ed.2d 621 (2005), altering significantly the legal context in which we must decide this appeal. Before Booker, we reviewed de novo whether a departure was proper under the constraints set forth in the United States Sentencing Guidelines (“U.S.S.G.” or “Guidelines”). See 18 U.S.C. § 3742(e). Now, instead, we review the district court’s sentence for “reasonableness.” Booker, 125 S.Ct. at 765-66. Also, whereas the district court was previously required to sentence according to the Guidelines, the Guidelines are now “effectively advisory.” Id. at 757.
The district court, of course, did not have the benefit of Booker and sentenced Defendant under the assumption that the Guidelines were mandatory. We conclude that the district court did not abuse its discretion by downwardly departing from the Guidelines. Moreover, even if the district court strayed from the departure authority available under the Guidelines, any error was harmless in view of the sentencing factors listed in 18 U.S.C. § 3553(a) (which the district court can now consider after Booker) and in view of our belief that the court would impose the same sentence again, having steadfastly maintained its position in the face of two opportunities to revise its sentence. Finally, we conclude that the resulting sentence was reasonable, and we affirm.
FACTUAL AND'PROCEDURAL BACKGROUND
Defendant began working as an administrative employee at the United States Attorney’s office in Los Angeles in 1990. In 2000, she was indicted on 10 counts of theft of government funds, mail fraud, and wire fraud. She pleaded guilty to one count of mail fraud and admitted to having used government credit cards for unauthorized personal purchases of between $350,000 and $500,000.
At sentencing, the parties agreed with the probation office that Defendant’s offense level was 16 and that her Criminal History Category was I, resulting in a sentencing range of 21 to 27 months. Defendant requested, and the government opposed, a six-level downward departure because of Defendant’s family circumstances and mental and emotional condition. In support of her request, Defendant produced the evaluation of Dr. Barbara Cort Counter, a forensic psychologist.
Dr. Counter characterized Defendant as suffering from “severe symptoms of post-traumatic stress” occasioned by two events: her abandonment by her parents ás a child and the violent murder of her fiancé, the bloody aftermath of which she witnessed while five months pregnant with their child in 1989. Defendant’s theft offense, according to Dr. Counter, was part of a “manic denial of psychic trauma, accompanied by compulsive coping behaviors.” Dr. Counter had evaluated Defendant for three-and-one-half hours, administered and reviewed a psychological test, spoken with Defendant’s counsel, and reviewed letters submitted by Defendant’s family members. Defendant made Dr. Counter available for cross-examination, [695]*695which the government declined at the first sentencing hearing. Nor did the government offer any expert psychological testimony of its own.
Defendant also argued for a departure because of the unusually important role that she played in the life of her daughter, who was 11 years old at the time of the first sentencing hearing in 2001. Since the murder of her fiancé, Defendant has been the sole parent and the primary source of financial support for her daughter.
After hearing argument, the district court departed downward by eight levels, resulting in a sentencing range of zero to 6 months. The court sentenced Defendant to five years of probation, upon the condition that she serve 40 days of her probation, on consecutive weekends, in “a jail-type institution.” The court also ordered restitution totaling $435,918, plus 3,000 hours of community service. In addition, Defendant was prohibited from applying for a loan or line of credit without the prior approval of the probation office.
The government appealed, and we vacated the sentence and remanded for re-sentencing because the district court had given no reasons for “the direction and the degree of the departure.” Meny-tueather I, 36 Fed.Appx. at 263. After that first remand, the district court denied the government’s motions for an independent psychological evaluation of Defendant and additional investigation by the probation office, ruling that those procedures could have been, but were not, requested at the initial sentencing. After a hearing at which the government cross-examined Dr. Counter, the court reaffirmed its previous sentence. In support of the sentence, the court recited and adopted specific findings of fact and conclusions of law, as well as noting that it relied on Defendant’s post-conviction rehabilitation.
In Menyweather II, we again vacated the district court’s sentence and remanded, holding that the court (1) erred in relying on post-conviction rehabilitation without giving notice to the government, and (2) failed to explain the extent of the departure, as distinct from the bases for departure. 69 F. App’x 874-75. On remand, the district court again denied the government’s request for further development of the record and reaffirmed its sentence. In support of the sentence, the court adopted expanded findings of facts and conclusions of law that included citations to cases in which downward departures of comparable degree had been affirmed. The court eliminated its earlier reliance on post-conviction rehabilitation.
The government timely appealed the sentence.
LEGAL STANDARDS AND STANDARDS OF REVIEW
In the wake of Booker, federal sentencing is now governed by 18 U.S.C. § 3553(a), which states that district courts “shall consider” the following factors:
(1) the nature and circumstances of the offense and the history and characteristics of the defendant;
(2) the need for the sentence imposed—
(A) to reflect the seriousness of the offense, to promote respect for the law, and to provide just punishment for the offense;
(B) to afford adequate deterrence to criminal conduct;
(C) to protect the public from further crimes of the defendant; and
(D) to provide the defendant with needed educational or vocational training, medical care, or other correctional treatment in the most effective manner;
(3) the kinds of sentences available;
[696]*696(4) the kinds of sentence and the sentencing range established for—
(A) the applicable category of offense committed by the applicable category of defendant as set forth in the guidelines—
(i) issued by the Sentencing Commission pursuant to section 994(a)(1) of title 28, United States Code ...; and
(ii) that, except as provided in section 3742(g), are in effect on the date the defendant is sentenced; or
(B) in the case of a violation of probation or supervised release, the applicable guidelines or policy statements issued by the Sentencing Commission pursuant to section 994(a)(3) of title 28, United States Code ...;
(5) any pertinent policy statement—
(A) issued by the Sentencing Commission pursuant to section 994(a)(2) of title 28, United States Code ...; and
(B) that, except as provided in section 3742(g), is in effect on the date the defendant is sentenced.
(6) the need to avoid unwarranted sentence disparities among defendants with similar records who have been found guilty of similar conduct; and
(7) the need to provide restitution to any victims of the offense.
As the Supreme Court pointed out in Booker, § 3553(a) makes the Guidelines sentencing range a required consideration, see § 3553(a)(4), but “permits the court to tailor the sentence in light of other statutory concerns as well.” Booker, 125 S.Ct. at 757; see also id. at 767 (“The district courts, while not bound to apply the Guidelines, must consult those Guidelines and take them into account when sentencing.”).
Like many other circuits, we have thus continued to address challenges to a district court’s interpretation and application of the Guidelines because, although the district court is not bound by the Guidelines, it still should “consult them for advice as to the appropriate sentence.” United States v. Kimbrew, 406 F.3d 1149, 1152 (9th Cir.2005) (citing Booker, 125 S.Ct. at 767). Several of our sister circuits have held that, to comply with Booker’s mandate that district courts “take [the Guidelines] into account when sentencing,” 125 S.Ct. at 767, courts normally must determine and consider the correct Guidelines range. See, e.g., United States v. Haack, 403 F.3d 997, 1002-03 (8th Cir.), cert. denied, — U.S.-, 126 S.Ct. 276, 163 L.Ed.2d 246 (2005); United States v. Crosby, 397 F.3d 103,111-12 (2d Cir.2005). Also, because § 3553(a)(5) demands consideration of the Sentencing Commission’s policy statements, courts likewise must consider whether the Guidelines provide authority to depart. Haack, 403 F.3d at 1002; Crosby, 397 F.3d at 113; see also United States v. Jackson, 408 F.3d 301, 305 (6th Cir.2005) (holding that consideration of advisory Guidelines provisions, including departures, is required); United States v. Crawford, 407 F.3d 1174, 1183 (11th Cir.2005) (remanding because grounds for departure were impermissible under the Guidelines). An error in determining the Guidelines range, or in understanding the authority to depart from that range, can prevent district courts from properly considering the Guidelines. See, e.g., United States v. Selioutsky, 409 F.3d 114, 118 (2d Cir.2005) (“An error in determining the applicable Guideline range or the availability of departure authority would be the type of procedural error that could render a sentence unreasonable under Booker.”); Crawford, 407 F.3d at 1183 (“true consultation cannot be based on an erroneous understanding of the Guidelines”). Thus, if the sentence imposed resulted from an incorrect application of the Sentencing Guidelines, and the error was not harmless, ordinarily we will remand to [697]*697the district court for further sentencing proceedings, permitting the district court on remand to consider the proper Guidelines sentence along with other sentencing factors. Kimbrew, 406 F.3d at 1153; see also United States v. Riggs, 410 F.3d 136, 136-37 (4th Cir.2005); Crawford, 407 F.3d at 1183; Haack, 403 F.3d at 1003.
In this ease, the first question is whether the district court began with the correct Guidelines sentence. With respect to that question, the usual standards of review apply: “[We] review[] the district court’s interpretation of the Sentencing Guidelines de novo, the district court’s application of the Sentencing Guidelines to the facts of this case for abuse of discretion, and the district court’s factual findings for clear error.” Kimbrew, 406 F.3d at 1151. The parties agreed, and we see no error in their agreeing to, the Guidelines range of 21 to 27 months.
The second question is whether the district court properly understood its authority to depart downward under the then-mandatory Guidelines. Because Booker excised the de novo review of departures previously mandated by 18 U.S.C. § 3742(e), 125 S.Ct. at 765, we hold that the appropriate standard for reviewing the district court’s determination of its departure authority is abuse of discretion, see Koon v. United States, 518 U.S. 81, 98-100, 116 S.Ct. 2035, 135 L.Ed.2d 392 (1996), the standard in place before the statutory de novo review was enacted in 2003.1 Accord Selioutsky, 409 F.3d at 119 (holding that abuse of discretion is the appropriate standard for reviewing, as an element of reasonableness review, whether a departure is permissible under the Guidelines).
We conclude that, under this standard of review, the district court did not abuse its discretion by departing downward for diminished capacity under U.S.S.G. § 5K2.13 or by departing downward for family circumstances under U.S.S.G. § 5H1.6. Alternatively, even if the district court abused its discretion by departing downward under the Guidelines, we hold that any error was rendered harmless in this case by the court’s expanded authority to consider circumstances related to the sentencing factors in 18 U.S.C. § 3553(a).
DISCUSSION
A. The district court did not abuse its discretion by departing downward for “diminished capacity” under U.S.S.G. § 5K2.13.
The Sentencing Guidelines identify “diminished capacity” as a factor that may not have been considered adequately by the Sentencing Commission in promulgating the Guidelines — that is, as an encouraged factor for departure.2 U.S.S.G. §§ 5K2.0, 5K2.13. Under the version of § 5K2.13 in effect at the time of Defendant’s first sentencing in 2001, a departure is appropriate if “the defendant committed the offense while suffering from a significantly reduced mental capacity,” defined as
[698]*698a significantly impaired ability to (A) understand the wrongfulness of the behavior comprising the offense or to exercise the power of reason; or (B) control behavior that the defendant knows is wrongful.
U.S.S.G. § 6K2.13. cmt. n. 1 (2000).3 This court has held that post-traumatic stress disorder can be the basis for a departure under § 5K2.13 if the “ailment distorted[Defendant’s] reasoning[,] interfered with [her] ability to make considered decisions,” and contributed to the commission of the offense in some way. United States v. Cantu, 12 F.3d 1506, 1513, 1515 (9th Cir.1993).
The district court found that Defendant suffers from post-traumatic stress disorder and concluded that, because that disorder contributed to her offense conduct, a departure was warranted under § 5K2.13. In reaching its conclusion, the district court did not clearly err by crediting the detailed opinion of a licensed psychologist, in preference to the government’s arguments that the psychologist was mistaken or had insufficient information on which to base her conclusion. The government did not challenge Dr. Counter’s qualifications, nor did the government offer rebuttal evidence from another psychologist. Although the government’s counsel presented persuasive arguments,4 the district court was not required to accept those arguments. The district court had the opportunity to evaluate Dr. Counter’s credibility under cross-examination, and we cannot say that the court clearly erred by finding her credible and by accepting her opinion that Defendant’s chronic symptoms of post-traumatic stress were linked to her inability to make reasoned decisions and to her compulsive acquisition behavior.
In view of that finding of fact, which is not clearly erroneous, the court did not abuse its discretion by finding a departure appropriate under U.S.S.G. § 5K2.13. In Cantu, we interpreted § 5K2.13 to require that an “ailment distorted [Defendant’s] reasoning[,] interfered with [her] ability to make considered decisions[,]” and contributed to the commission of the offense in some way.5 12 F.3d at 1513, 1515; see also United States v. Thompson, 315 F.3d 1071, 1079 (9th Cir.2002) (Berzon, J., concurring) (discussing 1998 amendment to [699]*699§ 5K2.13, expressly permitting courts to consider volitional impairments).
B. Even if the court abused its discretion under U.S.S.G. § 5H1.6, any error was harmless.
Unlike diminished capacity, family circumstance is a discouraged factor under the Guidelines, which state that “family ties and responsibilities and community ties are not ordinarily relevant” in determining whether a departure is warranted. U.S.S.G. § 5H1.6 (2000);6 see also United States v. Aguirre, 214 F.3d 1122, 1127 (9th Cir.2000) (referring to family circumstance as a “discouraged” factor). A discouraged factor may be grounds for departure under the Guidelines if it is “present to an exceptional degree or in some other way makes the case different from the ordinary case where the factor is present.” Koon, 518 U.S. at 96, 116 S.Ct. 2035. To determine whether Defendant’s family circumstances are extraordinary, we compare this case to others in which district courts have granted downward departures under § 5H1.6, being mindful that some of our cases were decided under de novo, rather than abuse of discretion, review.
In United States v. Leon, 341 F.3d 928, 931 (9th Cir.2003), we commented that downward departures based on § 5H1.6 “generally involve situations where the defendant is an irreplaceable caretaker of children, elderly, and/or seriously ill family members.” We concluded, on de novo review, that a departure was proper because of the particular nature of the defendant’s wife’s ailments and the unique physical, material, and emotional support that the defendant provided. Id. at 933. In Aguirre, applying the abuse of discretion standard, we upheld a four-level downward departure where the death of the defendant’s husband left their eight-year-old son without a custodial parent. 214 F.3d at 1127. We declined to “second guess the district court’s determination that this case involved an unusual family situation.” Id.
By contrast, in United States v. Miller, 991 F.2d 552, 553 (9th Cir.1993), and United States v. Berlier, 948 F.2d 1093, 1096 (9th Cir.1991), on de novo review, we held that downward departures were not appropriate because there was nothing unusual about the family situations presented. In each case, the children had another parent to care for them while the defendants were incarcerated. See Miller, 991 F.2d at 556 (Tang, C.J., concurring in part and dissenting in part); Berlier, 948 F.2d at 1096.
The conclusions that we reached in Leon, Aguirre, Miller, and Berlier are consistent with the First Circuit’s view that, when evaluating departures for family responsibilities under § 5H1.6, courts should assess the nature of the care that the defendant provides to his or her family members and determine whether “there are feasible alternatives of care that are relatively comparable” to the defendant’s. United States v. Roselli, 366 F.3d 58, 68-69 (1st Cir.2004) (internal quotation marks omitted). Here, the district court essentially concluded that the relationship between Defendant and her daughter was so unusual that care by others was not feasible:
This case does not simply involve a single mother and child. The facts and circumstances show unusual traumatic circumstances for this mother and child and an unusual relationship between the two. This mother has been the sole parent caring for the child at home and after school. The mother has been consistently employed since the child’s birth and her primary source of financial sup[700]*700port. The social security benefits the child receives monthly (less than $400) are minimal and insufficient to support a child. [Defendant] has a special relationship with this child who has already lost one parent and has never been without her sole surviving parent excluding absences during brief trips.
The court also relied on the fact that, although Defendant’s grandmother and great-aunt live nearby, their housing situation is unsafe.
Were we reviewing de novo, we would conclude that Defendant did not prove that she provides care that is irreplaceable or that could not feasibly be provided by another. Under an abuse of discretion standard, however, we hesitate to “second guess” the district court’s conclusion that Defendant’s relationship with her daughter, and the care that Defendant provides, are unusual as compared with the situation of other single parents. As we did in Aguirre, 214 F.3d at 1127, we'acknowledge that district courts are “particularly suited” to determine whether a factor makes a case unusual, because they are “informed by [their] vantage point and day-to-day experience in criminal sentencing,” Koon, 518 U.S. at 98, 116 S.Ct. 2035. We therefore conclude that the district court did not abuse its discretion by downwardly departing under § 5H1.6.
Alternatively, even if we were to accept the government’s argument that the district court erred by departing on this basis under the Guidelines, we can say confidently that any error would be harmless to the government in this case. This is because, under the unusual circumstances present in this third-time appeal, we recognize that the district court could — and would — impose the same sentence again under the now-advisory Guidelines regime.
In the “broader appraisal,”7 available to district courts after Booker, courts can justify consideration of family responsibilities, an aspect of the defendant’s “history and characteristics,” 18 U.S.C. § 3553(a)(1), for reasons extending beyond the Guidelines. “District courts now ... have the discretion to weigh a multitude of mitigating and aggravating factors that existed at the time of mandatory Guidelines sentencing, but were deemed ‘not ordinarily relevant,’ such as age, education and vocational skills, mental and emotional conditions, employment record, and family ties and responsibilities.” United States v. Ameline, 409 F.3d 1073, 1093 (9th Cir. 2005) (en banc) (Wardlaw, J., concurring in part and dissenting in part) (emphasis added). The difficulty of providing appropriate care for a child of a single parent may, when balanced against factors such as the nature of the offense, § 3553(a)(1), deterrence to criminal conduct, § 3553(a)(2)(B), and protection of the public, § 3553(a)(2)(C), warrant a sentence outside the Guidelines.
Furthermore, as we have said, we have no doubt that the district court would impose the same sentence under the advisory Guidelines regime, as the district court has imposed the identical sentence three times already. See Selioutsky, 409 F.3d at 118 n. 7 (noting court arguably could forego review of the correctness of the departure under the Guidelines if it had a “sufficient basis for believing that the same sentence would have been imposed as a non-Guidelines sentence,” because “any error in using departure authority to select the sentence that was imposed [701]*701would be harmless”). The district court clearly believed that, in this case, the potential harm to the close relationship between this single parent and her child outweighed the benefits of a prolonged period of incarceration to achieve deterrence, protection of the public, and punishment. Indeed, the court stated that the conditions of Defendant’s probation were “as strenuous as any other sentence ■ I could impose.” Cf 18 U.S.C. § 3553(a)(3) (directing courts to consider “the kinds of sentences available”). We also observe that the district court’s goal of obtaining restitution for the victims of Defendant’s offense, 18 U.S.C. § 3553(a)(7), is better served by a non-incarcerated and employed defendant. In sum, family circumstances were a permissible consideration here — if not under the Guidelines, then as part of a balancing of factors under § 3553(a).
C. The length of the sentence was reasonable, considering the combination of factors.
Finally, we turn to the government’s objections to the length of the sentence (or, more precisely, to the extent of the downward departure from the Guidelines offense level). In post -Booker parlance, this is essentially a challenge to the “reasonableness” of the ultimate sentence.
As a threshold matter, the government contends that the district court failed to give reasons for the extent of its departure from the Guidelines and, thereby, failed to comply with our mandate in Menyweather II. We agree that, after Booker, the district court still is “required to articulate the reasons for the extent of the departure in sufficiently specific language to allow appellate review.” United States v. Working, 224 F.3d 1093, 1102 (9th Cir. 2000) (en banc) (internal quotation marks omitted); see 18 U.S.C. § 3553(c) (requiring a statement of reasons for the particular sentence imposed); see also Crosby, 397 F.3d at 116 (noting that § 3553(c) was not excised by the Supreme Court in Booker).
But we do not agree that the district court failed to explain the extent of its departure here. In response to our remand in Menyweather II, the district court explained the extent of its departure from the Guidelines by supplementing its factual findings and, for each factor on which it based its decision to depart, citing and describing several other cases in which courts had departed downward on similar facts. Although the court did not make express comparisons between Defendant’s case and the cited cases, the cited cases are facially similar and their presence alone implies that a comparative analysis led the court to select an eight-level departure. More importantly, as this court required in Working, 224 F.3d at 1102, the supplemented factual findings and comparative citations provide a basis for us to review, on the merits, whether the length of the sentence was reasonable.
Even before Booker, our task was to determine whether the extent of a departure was reasonable, so our cases applying abuse of discretion review to that question remain relevant after Booker. See United States v. Alfaro, 336 F.3d 876, 881 (9th Cir.2003) (citing 18 U.S.C. § 3742(e)(3) and reviewing for abuse of discretion whether the extent of a departure was reasonable); United States v. Working, 287 F.3d 801, 806 (9th Cir.2002) (same). We commonly have performed that review by comparing the defendant’s case with other published cases in which departures have been affirmed. See, e.g., United States v. Green, 105 F.3d 1321, 1323 (9th Cir.1997). In Green, we noted that departures for a particular factor had generally ranged between one and five levels; therefore, we [702]*702concluded that a 15-level departure was an abuse of discretion. Id.
Our cases show that downward departures for diminished capacity generally range between one and four levels. See, e.g., United States v. Malley, 307 F.3d 1032, 1033-34 (9th Cir.2002) (five-level departure; combination of diminished capacity and extraordinary acceptance of responsibility); United States v. Garza-Juarez, 992 F.2d 896, 913 (9th Cir.1993) (four-level departure; combination of the defendant’s panic disorder with agoraphobia and coercion under § 5K2.12); United States v. Lewinson, 988 F.2d 1005, 1007 (9th Cir. 1993) (four-level departure under § 5K2.13 for long-standing psychological problems was “well within line with other adjustments established by the guidelines for various mitigating factors indicating diminished culpability”). Downward departures for extraordinary family circumstances most often fall within a similar range. See, e.g., Leon, 341 F.3d at 929, 933 (six-level departure); Aguirre, 214 F.3d at 1128 (four-level departure); Roselli, 366 F.3d at 67, 70 (three-level departure).
Considering those cases, and the sentencing factors in § 3553(a), we cannot say that an eight-level downward departure for the combined effect of two factors — Defendant’s diminished capacity and family circumstances — was unreasonable. The. district court expressly justified its sentence of probation by saying that it viewed the conditions of probation as very “strenuous,” yet without causing a significant disruption of the parent-child relationship. The nature of the offense was not such that incarceration, as distinct from strict controls on Defendant’s financial activities, was necessary to protect the public or afford deterrence. See 18 U.S.C. § 3553(a)(2); cf. Working, 287 F.3d at 809 (remanding because the “court’s reasoning was insufficient to justify a departure that resulted in no sentence at all for a serious crime of violence”). Also, as we have mentioned, a sentence of probation may have made Defendant better able to provide restitution to the victims of her crime, see 18 U.S.C. § 3553(a)(7).
Although we are unlikely to have selected this particular sentence if we were doing the sentencing, that is not our function. In these circumstances, we find no abuse of discretion in the sentence (upon Defendant’s conviction for a single count of mail fraud) consisting of five years of probation, on the condition that Defendant serve 40 days in jail on consecutive weekends; plus $435,918 in restitution, to be paid first to the individual victim; plus 3,000 hours of community service; plus a prohibition from applying for a loan or line of credit without the prior approval of the probation office.
AFFIRMED.