
519 P.2d 1131 (1974)
Gerda M. HORTON, Appellant,
v.
George D. HORTON, Appellee.
No. 1825.
Supreme Court of Alaska.
March 18, 1974.
John E. Reese and Bruce C. Twomley, of Alaska Legal Services Corp., Anchorage, for appellant.
James R. Clouse, Jr., Anchorage, for appellee.
Before RABINOWITZ, C.J., and CONNOR, BOOCHEVER and FITZGERALD, JJ.

OPINION
CONNOR, Justice.
Gerda M. Horton appeals from a post-divorce custody order issued by the superior court changing custody of the parties' 10-year old son, O'Brien, from the mother to the father.
The Hortons were married in Wiesbaden, Germany, in 1949. They came to Alaska in 1963 and have remained here to the present time. In 1967 they were divorced on the grounds of incompatibility of temperament.
The divorce was uncontested. Custody of their six children was awarded to Mrs. Horton.
*1132 In July of 1972, appellee George Horton moved to modify the divorce decree to award him custody of the two youngest children. Appellee subsequently withdrew his motion as to one of the two children, leaving only the custody of O'Brien Horton, then age 10, in issue. Mrs. Horton contested the motion, and a hearing ensued before the superior court. That court granted Mr. Horton's motion and modified the divorce decree to award care, custody, and control of O'Brien to him. At the same time the court granted Mrs. Horton reasonable visitation rights. Mrs. Horton appeals the modification of custody.
Before we reach the substantive issues raised in this appeal, there is one procedural hurdle to be cleared. Mr. Horton contends that this court is without jurisdiction to hear the appeal because Mrs. Horton (1) failed to post bond on appeal, and (2) moved for appeal at public expense[1] (a) without giving him notice of the hearing on the motion and (b) without showing the "merits of the appeal" and that the "interests of justice" required such an appeal. Mr. Horton's contention is utterly without merit. It is, of course, not necessary for an appellant to post bond if an appeal at public expense is granted. Mrs. Horton's motion for appeal at public expense was timely made and was properly supported by affidavit. The motion was granted by the superior court at an appeal conference where both sides were represented by counsel and objections to the granting of the motion were made by counsel for appellee. We have reviewed the record and are satisfied that the appeal was meritorious and in the interests of justice and that Mrs. Horton's motion was properly granted.
Turning to the merits of this appeal, Mrs. Horton argues that the lower court abused its discretion in finding (1) that Mr. Horton is a fit and proper parent to have custody of his minor child and (2) that the best interests of the child would be accommodated by awarding Mr. Horton custody of the child.
Child custody determinations are among the most difficult in the law. Grave responsibility is placed upon the trial courts faced with making these determinations and, at the same time, broad discretion is granted them. However, while "great weight must be accorded to the trial judge's experience and to his evaluation of demeanor testimony,"[2] his discretion is not unlimited. On review we must determine whether that discretion has been abused, perhaps by assigning too great a weight to some factors while ignoring others, perhaps by elevating the interests of one of the parties to the dispute above that of the child, perhaps by making a clearly erroneous finding with respect to some material issue, or perhaps in some other manner.
It is well established that on appeal our task is to ascertain whether or not the trial court misapplied the broad discretion vested in it in regard to determination of custody questions, and whether the court's findings in respect to custodial issues are clearly erroneous. Sheridan v. Sheridan, 466 P.2d 821, 824 (Alaska 1970). (footnotes omitted)
A court modifying a previous custody determination must be guided by what appears to be for the best interests of the child.[3] In the present case, we find that the lower court abused its discretion in modifying custody.
*1133 At the modification hearing, counsel for appellant offered the testimony of the Horton's two oldest daughters to the effect that (1) their father had engaged in incestuous relations with them from their childhood until their parents' separation prior to their 1967 divorce; (2) their father attempted to physically induce his oldest son, their brother, to have sexual intercourse with them when they were very young (apparently between the ages 6 and 10); and (3) appellee's most recent sexual advance toward his oldest daughter occurred in 1970, after his remarriage, when she was 19 years old. Rather than hear this testimony, the trial court stated that it would accept the above allegations as proven facts for the purpose of this custody dispute. Appellee agreed to this, giving up his right to cross-examination rather than have his daughters testify. It should be noted, however, that the trial court also told appellee that the court would take as accepted appellee's denial of ever having engaged in any of the alleged conduct.[4] Nevertheless for the purposes of this appeal, we treat the above allegations as proven facts.
No evidence of rehabilitation was presented by appellee. There is nothing in the record to indicate that appellee has sought to correct his malady or that his malady has disappeared.
The superior court apparently chose to ignore the absence of any evidence of rehabilitation and instead chose to rely on the passage of two years time since the last incident plus appellee's remarriage to serve as protection against the recurrence of "such problems." In so doing, the superior court erred.
It is not to be assumed absent some evidence of rehabilitation that appellee no longer suffers from his particular malady. Common sense prohibits us from concluding merely because two years have passed since the last reported incident, that a problem like that of appellee's has disappeared. Similarly it seems almost self-evident that a person with such a problem would be of questionable fitness to have custody of a child of either sex or almost any age. The manner in which appellee treated his other children is certainly relevant to a determination of the best interests of the child whose custody is presently at issue. Assuming, as we must in the absence of any evidence or any authority to the contrary, that appellee still suffers from this sexual problem, we cannot find that it would be in the child's best interest to be placed in appellee's custody.
Nearly the sole basis for the superior court's preference for the father over the mother in this case was the court's belief that a 10-year old boy like O'Brien needs "a father figure."[5] Given that the trial court *1134 accepted as fact appellee's sexual abuse of his older children, it was an abuse of discretion to find that it was in the child's best interests to be placed in the custody of appellee without ample evidence of appellee's rehabilitation.
We reverse and direct that custody of the child be restored to appellant.
Reversed.
ERWIN, J., not participating.
NOTES
[1]  The motion was pursuant to S.Ct.R 43(a), now App.R. 35(a), both of which read in pertinent part as follows:

Where the merits of the appeal or petition and the interests of justice require, the superior court may authorize an appeal or petition for review in a civil matter, without the prepayment of fees and costs or the giving of security therefor by a person who has been determined to be financially unable to pay such fees or costs or to give security.
[2]  Sheridan v. Sheridan, 466 P.2d 821, 824 (Alaska 1970).
[3]  AS 09.55.205.
[4]  It was with that understanding that appellee agreed to give up his right to cross-examination, ostensibly in order that his children not have to become involved in the hearing.
[5]  The superior court indicated that it found both appellant and appellee to be "fit and proper parents" capable of providing "a stable home." In appellant's favor was the fact that in her home O'Brien would have the benefit of being raised with his younger sister. Balanced against this and apparently outweighing it was the fact that in appellee's home, O'Brien would have the benefit of two adults, including (and most important to the trial judge) a "father figure" in the person of appellee.

The trial court's determination that the balance turned in favor of the father on these facts is, we believe, a questionable conclusion even without the sexual problems presently involved. We must emphasize that it is a change in custody that is involved here and that such changes in custody are not to be lightly made.
Children should not be shuttled back and forth between divorced parents unless there are important circumstances justifying such change as in their best interests and welfare. Nichols v. Nichols, 516 P.2d 732, 735 (Alaska 1973).
Granting such overriding importance to the "father figure" concept is especially dubious in a case like the present where changing custody will mean separating a child from his siblings. In other cases we have noted the importance of "not separating the children unless their welfare clearly requires such a course." Nichols v. Nichols, 516 P.2d 732, 736 (Alaska 1973).
[C]onsideration should be given to the desirability of keeping the children of the family together so that they may enjoy the normal condition of childhood of growing up together as brother and sisters. Rhodes v. Rhodes, 370 P.2d 902, 903 (Alaska 1962). (footnotes omitted)
