
760 P.2d 501 (1988)
R.C. and T.C., Parents, Appellants/Cross-Appellees,
v.
STATE OF Alaska, DEPARTMENT OF HEALTH AND SOCIAL SERVICES, Appellees/Cross-Appellants.
Nos. S-2363, S-2386 and S-2410.
Supreme Court of Alaska.
August 12, 1988.
*502 Daniel L. Callahan, Schendel & Callahan, Fairbanks, for appellant/cross-appellee, T.C.
Susan Downie, Asst. Public Defender, Fairbanks, and Dana Fabe, Public Defender, Anchorage, for appellant/cross-appellee, R.C.
D. Rebecca Snow, Asst. Atty. Gen., Fairbanks, Grace Berg Schaible, Atty. Gen., Juneau, for appellees/cross-appellants.
Gerard R. LaParle, Law Firm of Gerard R. LaParle, Fairbanks, guardian ad litem for Minor Children.
Before MATTHEWS, C.J., and RABINOWITZ, BURKE, COMPTON and MOORE, JJ.

OPINION
BURKE, Justice.
This appeal is from an order terminating the parental rights of T.C. (mother) and R.C. (father) to four minor children, and giving custody to the Department of Health and Social Services (Department).

I
The C. family consists of the parents, two thirteen-year-old twin girls from the mother's previous marriage, and two boys from the current marriage, ages nine and six.[1] The Department has been in contact with the family since July, 1981. It has dealt with problems of alcohol-related domestic violence between the mother and father, the girls' excessive absences from school, and the mother's failure to obtain prenatal care during her pregnancy.
In February, 1982, the Department arranged for a public health nurse to begin visiting the family home regularly to (1) ensure that the girls were sent to school instead of babysitting their brother, (2) help with the mother's pregnancy, and (3) help improve the household in terms of nutrition and hygiene. Several months later, the nurse notified the Department of her concern about the infant son's failure to grow. The mother had not had prenatal care, and the boy had not seen a doctor since his birth. The parents told the Department that they had not had the child treated because they felt they could not pay for medical treatment. They agreed to give temporary custody to the Department so it could pay for their son's hospitalization.
After this, the Department arranged for a social worker to begin home visits, and also arranged for psychological evaluations of the parents. The doctor found the mother to be functioning at an intellectually borderline level, very defensive and frightened, and unable to admit to her problems. The father was found to be defensive and suffering from a schizotypal personality disorder. The Department continued to provide support services to help the parents with their marital problems, the father with his alcohol and violence problems, and the mother with her agoraphobia and other problems.
On July 21, 1983, the Department assumed emergency custody of the three older children.[2] This action was prompted by a report from the Alaska State Troopers that the father was drinking and threatening the girls, and had slammed one girl's leg in the trailer door. The next day, the mother and father went to a temporary custody hearing where the court appointed a guardian ad litem for the children and *503 separate counsel for each parent.[3] The court granted the Department 30 days temporary custody based on the several-year history of drinking, violence, and basic neglect of the children.
During the following thirty days, the parents stipulated to an extension of the temporary custody so that the Department could "complete its investigation and evaluation ... and to allow time for the parties to ... agree on a case plan." After more family analysis was done, it was determined that the parents' "[a]bility to fulfill the developmental needs of their children [was] severely impaired." Before the temporary custody expired, the parents (with their attorneys), the guardian, and the social worker stipulated to a second extension of custody, agreeing that the children were in need of aid, and that their best interests would be served by extending the Department's custody for up to two years, or until September 23, 1985. The stipulation also provided a detailed plan for services, including psychiatric testing, homemaker services, a public health nurse, regular therapy, and meetings with the social worker.[4]
In October, 1984, the Department petitioned the court for termination of parental rights under AS 47.10.080(c)(3), asserting that the parental conduct which had caused the children to be adjudicated children in need of aid in September, 1983, was likely to continue if parental rights were not terminated.[5] The two-phase hearing on this petition was held January 28 to February 1, 1985. Several days into the hearing, the trial judge told the parties that based on the evidence thus far, he had "no question" that there were on-going "substantial problems" with the family, but that he
would have some difficulty at this point in time in terminating the rights just because of the time involved... . [T]he court has some difficulty in not giving the parents some additional time to see if, in fact, the situation corrects itself. Obviously, if the situation can't correct itself, the rights have to be terminated. I don't think there's any question about that.
The parties then took some time to negotiate a new stipulation containing a detailed plan for services and counseling for the parents, with the goal of reuniting the family within one year. This stipulation contained an adjudication provision stating that the children were in need of aid by clear and convincing evidence. It further provided that review hearings to check on the parents' progress would occur after three, six, nine, and twelve months, and that the Department's custody of the four children would be extended for up to two more years. The court signed this stipulation on February 15, 1985.
The mother and father subsequently attended the required counseling sessions, visited the children, and made efforts to improve. During the short periodic review hearings, however, the Department stated several times that it thought the parents were not progressing adequately (since they were still unable to meet the children's needs), and that it intended to continue the proceedings and seek termination.
No twelve-month review hearing was held in February, 1986. In April, the mother moved for a review hearing and asked that her children be returned home. In response, the Department moved for an order requiring the mother and father to undergo a psychological examination by a disinterested doctor because it was "still unclear whether the children should be returned to their parents' care or whether the termination proceeding should be set on."[6] The court granted the motion, and, after the doctor submitted her report, the Department *504 informed the court that it intended to continue with the disposition phase of the termination trial. Due to scheduling difficulties, the actual hearing was postponed until October, 1986.
At the October termination hearing, the court relied on the February 15, 1985 stipulation as proof that the children were in need of aid. After several days of testimony, the court found that the Department had proven by clear and convincing evidence that the parental conduct that caused the children to be in need of aid was likely to continue, and thus terminated the parents' rights.
The mother and father appeal.

II
Termination of parental rights under AS 47.10.080(c)(3)[7] is a two-step process. The court must find by clear and convincing evidence (1) that there is a child in need of aid under AS 47.10.010(a)(2) as a result of parental conduct, and (2) that the parental conduct is likely to continue. E.J.S. v. State, 754 P.2d 749, at 750 (Alaska 1988); K.T.E. v. State, 689 P.2d 472, 475 (Alaska 1984). The burden of proof is on the state. K.T.E., 689 P.2d at 476. Here, the court found that the children were in need of aid under AS 47.10.010(a)(2)(A), which provides:
(a) Proceedings relating to a minor ... are governed by this chapter ... when the court finds the minor
... .
(2) to be a child in need of aid as a result of
(A) the child ... having no parent, guardian, custodian or relative caring or willing to provide care... .
"Caring" is defined in AS 47.10.290(1):
"caring" under AS 47.10.010(a)(2)(A) means to provide for the physical, emotional, mental, and social needs of the child[.]

A. The Stipulation

The parties agreed to the February 15, 1985 stipulation midway through the first hearing on the Petition to Terminate Parental Rights. Paragraph four of the stipulation states:
Based on the evidence presented, there is clear and convincing evidence that the children are children in need of aid under AS 47.10.010(a)(2)(A) and 47.10.080(c)(3) as a result of the conduct of the parents.
At the second hearing, in October, 1986, the trial court decided that the state could "rely on the testimony [from the previous hearing] and the stipulation to meet their burden that the children are children in need of aid."
The mother argues that the court erred in giving any effect to paragraph four at the second termination hearing because the terms of the stipulation regarding the adjudication were limited to a one-year period.[8] She relies on other terms of the stipulation which contemplated change "within one year," and provided that "[a]t the one-year hearing, final action shall be taken on the Petition to Terminate Parental Rights."
We are not persuaded by the mother's arguments. The court signed the February stipulation, thereby adopting as its own finding and conclusion that there was clear and convincing evidence that the children were in need of aid.[9] Paragraph four *505 includes no time limitation, and the references to the one-year period in other parts of the stipulation are simply unrelated to the adjudicatory paragraph. The period of time between the February, 1985 stipulation and the October, 1986 resumption of the termination hearing was simply an interruption between two phases of a single proceeding.[10] The stipulation itself refers to the Department's agreement to "postpone completion" of the disposition phase of the hearing. During the interruption, the court remained active in the case by means of the periodic review hearings. As a general rule, "[a] party may not challenge on appeal an order that he has agreed to in the trial court," L.L.M. v. P.M., 754 P.2d 262, 263 (Alaska 1988); accordingly, we conclude that the stipulation was valid at the time of the second hearing, and it was not erroneous for the trial court to rely on it.[11]

B. The Parental Conduct

In order to terminate parental rights, the Department must prove in the disposition hearing, by clear and convincing evidence, that the parental conduct which showed that the children were in need of aid is likely to continue to exist if there is no termination. AS 47.10.080(c)(3); see also Nada A. v. State, 660 P.2d 436, 440 (Alaska 1983). The mother argues that the evidence presented at the second trial showed a dramatic improvement in her behavior, and thus the court's conclusion that her conduct is likely to continue was erroneous. Likewise, the father argues that he and his wife "made significant progress" in terms of personal adjustments and parenting skills since February, 1985, and thus there was not clear evidence that his conduct is likely to continue.
We cannot say that the trial court's conclusion on this issue was clearly erroneous.[12] Although the parents did improve in some respects, virtually all of the professionals who worked with or evaluated them concluded that they had little or no ability to change. The parents were given abundant help and support in the five-year effort to reunite the family. However, they were simply unable to progress enough. The Department proved that their conduct was not likely to change, and the parents point to no persuasive facts that lead us to a "definite conviction" that a mistake has been made. Thus, we affirm.

C. Vagueness

The father argues that AS 47.10.010(a)(2)(A) and AS 47.10.290[13] are unconstitutionally vague, and therefore deny him due process of law as guaranteed by article 1, section 7 of the Alaska Constitution and the Fourteenth Amendment of the United States Constitution. He contends that the statutes are facially unconstitutional because they fail to give adequate notice of what conduct is prohibited.[14]
In determining whether a statute is unconstitutionally vague, we consider the following:
First, a statute may not be so imprecisely drawn and overbroad that it "chills" the *506 exercise of first amendment rights. The second consideration is that in order to be consistent with notions of fundamental fairness a statute must give adequate notice of the conduct that is prohibited. The final element in an analysis of statutory vagueness is whether the statute's imprecise language encourages arbitrary enforcement by allowing prosecuting authorities undue discretion to determine the scope of its prohibitions.
Summers v. Anchorage, 589 P.2d 863, 866-67 (Alaska 1979) (footnotes omitted). Factors two and three are relevant here: do the statutes give adequate notice of prohibited conduct, and do they encourage arbitrary enforcement?
In our view, the statutory scheme is not so vague as to deprive parents of their procedural due process rights; it gives the "person of ordinary intelligence a reasonable opportunity to know what is prohibited, so that he may act accordingly." Grayned v. City of Rockford, 408 U.S. 104, 108, 92 S.Ct. 2294, 2299, 33 L.Ed.2d 222, 227 (1972). As the Department argues, it would be impossible for the legislature to delineate every single possible behavior an unfit parent might exhibit, and still maintain a workable statutory scheme. See Thompson v. Arkansas Social Services, 282 Ark. 369, 669 S.W.2d 878, 882 (1984) (since particular disabilities of parents are diverse, it would be impossible to catalog each disability; the statute must be broad enough to encompass all proscribed behavior). The statute is as specific as it can usefully be, even though its application requires interpretation. We believe that the scheme accomplishes its purpose of protecting children, while balancing the parents' interests and still allowing reasonable flexibility for the exercise of discretion in the individual case.[15]
In addition, we note that several other states have upheld their statutory CINA schemes in the face of similar vagueness challenges.[16] The reasoning of the Colorado Supreme Court is apt:
The fact that the line separating those parents unwilling or unable to provide reasonable parental care from those having such willingness and ability may be difficult to draw is not a fatal defect. Such absence of litmus test precision is inherent in attempts to define conduct and conditions that make continuation of the parent-child legal relationship so detrimental to the child's physical or mental well-being as to be societally unacceptable.
In re M.S.H., 656 P.2d 1294, 1300 (Colo. 1983) (holding statute which allows termination where parent is "unfit" by failure to give "reasonable parental care" sufficiently definite and not violative of due process). We hold that the CINA statutes did not deprive the father of due process. They are not "so vague that [people] of common intelligence must necessarily guess at [their] meaning." State v. O'Neill Investigations, 609 P.2d 520, 531 (Alaska 1980).

D. Emergency Custody

The Department assumed emergency custody of the three oldest children on July 21, 1983 at 10:30 p.m. pursuant to AS 47.10.142. On the following day, the Department filed a Petition for Temporary Custody, and, on that same day, a hearing *507 was held.[17] The court gave the Department custody for up to thirty days, told the parents that it would appoint separate counsel for each of them, and allowed the father and mother to speak and ask several questions. The father argues that the procedure under AS 47.10.142 violates due process because it does not provide for judicial review of the Department's reasons for the initial taking of emergency custody.[18]
We reject the father's argument. The father did not object to any of the procedures at the hearing, and, within one month, his attorney signed a stipulation to extend the temporary custody. A month later, he and his attorney signed a second stipulation adjudicating his children to be in need of aid. These actions, along with any failure to raise this issue prior to appeal, constitute a waiver of any defects which may have occurred at the July, 1983 post-deprivation hearing. As we have stated,
[b]y consenting to certain procedures or by failing to object to others, a party may waive those rights which are arguably encompassed within due process guarantees.
In re C.L.T., 597 P.2d 518, 522 (Alaska 1979). Furthermore, this court has said that even if procedural defects existed in an earlier temporary custody hearing, they can be cured by a subsequent procedurally correct final dispositional hearing. D.E.D. v. State, 704 P.2d 774, 782 (Alaska 1985). Because the parents subsequently acknowledged, through stipulations, that their children were in fact in need of aid and that the Department should have custody of them, any alleged defects in the first temporary custody hearing were not "obviously prejudicial" to the point of plain error. See L.A.M., 727 P.2d at 1059. Thus, we find no due process errors requiring reversal.[19]

E. Visitation Rights

After the court decided that the state had presented clear and convincing evidence to justify termination of parental rights, the parties entered a stipulation regarding post-termination visitation, "reserving the right of the ... Department to challenge, in a cross appeal to any appeal on any ground by either parent," the legality of allowing such visitation. The stipulation allows the natural parents approximately three hours per month to visit the children, with whomever has legal custody deciding the degree of supervision. Further, the visits may be terminated by the custodian if they are not in the best interests of the children. The Department signed the stipulation and told the court that it believed it "will serve the interests of the children." The stipulation was subsequently included in the findings, conclusions and order which the court signed. The Department now argues that post-termination visitation is not allowed under our statutes.
Because the parties stipulated to the visitation plan, and it was therefore not "litigated" below, we will not consider the issue on appeal. Ordinarily, we "will not consider a claim of error if it was not both argued in the trial court and properly raised on appeal." L.A.M., 727 P.2d at 1059; Vest v. First Nat'l Bank of Fairbanks, 659 P.2d 1233, 1234 n. 2 (Alaska 1983). The state did purport to "reserve" its right to challenge the issue in a cross appeal if the parents appealed, but, nonetheless, *508 the issue was not "argued" below. Thus, we hold that the visitation stipulation, which was agreed by all parties to be in the children's best interest, is valid.

CONCLUSION
We AFFIRM the order of the trial court.
NOTES
[1]  The location of the girls' real father is unknown; his rights have been terminated as a result of his abandonment.
[2]  The youngest boy was left in the parents' custody, since there were no allegations that he had ever been hit or affected by the alcohol or violence.
[3]  The three oldest children have not lived with the mother and father since this occurrence in July, 1983.
[4]  During this time, one doctor's conclusion that the mother was unable to care for the youngest boy, who was still in her custody, led to an evaluation of that child. As a result, he, too, was removed from the parents' care in November, 1983 and placed in foster care with his siblings. All four children have been living together in the same foster home since then.
[5]  See infra note 7.
[6]  The children's guardian ad litem joined the state in this motion.
[7]  AS 47.10.080(c) provides:

If the court finds that the minor is a child in need of aid, it shall
... .
(3) by order, upon a showing in the adjudication by clear and convincing evidence that there is a child in need of aid under AS 47.10.010(a)(2) as a result of parental conduct and upon a showing in the disposition by clear and convincing evidence that the parental conduct is likely to continue to exist if there is no termination of parental rights, terminate parental rights... .
[8]  The mother does not challenge the validity of this finding in the stipulation (i.e., that the children were in need of aid by clear and convincing evidence) "for that point in time," but "only its efficacy 20 months after it was made."
[9]  The current version of the CINA Rules provides that parties may stipulate to any matter, including adjudication and disposition, and the court will accept such stipulations if it determines that the parties have consulted with counsel and understand their rights. Alaska CINA R. 14 (effective August 15, 1987). Here, the mother's attorney questioned her on the record to ensure that she understood the stipulation.
[10]  As the Department points out, the delay actually worked to the parents' benefit. The delay gave them more time to change their parental conduct, thus lowering the chances that the court would find that the parental conduct was likely to continue.
[11]  The court's treatment of the stipulation as "like a presumption," although perhaps erroneous, did not adversely affect the parents. Instead, the court gave them more leeway than it needed to. Thus, treating the stipulated finding as a rebuttable presumption was, at most, harmless error.
[12]  In reviewing the superior court's decision to terminate parental rights, we apply the clearly erroneous standard; we will not disturb the court's findings unless we are left with a definite and firm conviction that a mistake has been made. E.A. v. State, 623 P.2d 1210, 1212 (Alaska 1981).
[13]  See supra page 504.
[14]  This issue was not raised in the trial court. Thus, we review it for plain error. See In re L.A.M., 727 P.2d 1057, 1059 (Alaska 1986). To be plain, the error must affect substantive rights and be obviously prejudicial. Id.; see also In re C.L.T., 597 P.2d 518, 523 (Alaska 1979) (this court will consider plain error if it is so substantial as to result in a miscarriage of justice).
[15]  Termination of parental rights proceedings involve competing interests:

The parents' constitutional right to the care and custody of their children must be balanced against the rights of their children to an adequate home and education.
In re S.D., Jr., 549 P.2d 1190, 1201 (Alaska 1976).
[16]  See Miller v. Alabama Dep't of Pensions & Sec., 374 So.2d 1370, 1376 (Ala.App. 1979) ("unfit," "improper," and "neglected," not unconstitutionally vague); Thompson, 669 S.W.2d at 882 (statute does not define what "basic, essential and necessary needs" of child are, but is not unconstitutionally vague); Woodruff v. Keale, 64 Haw. 85, 637 P.2d 760, 766 (1981), ("care and support" clearly informs parents of what is required); In re Brooks, 228 Kan. 541, 618 P.2d 814, 820 (1980) ("unfit" is not unconstitutionally vague as previously construed by courts); State ex rel. Health & Social Servs. Dep't v. Natural Father, 93 N.M. 222, 598 P.2d 1182, 1185 (App. 1979) (parental "care and control" is subject to differing opinions as to what is necessary, but it nonetheless gives fair warning of what amounts to neglect); In re Daniel, 591 P.2d 1175, 1177 (Okla. 1979) ("proper parental care and guardianship" is not vague).
[17]  AS 47.10.142(d) requires a court hearing within 48 hours of taking emergency custody to determine whether probable cause exists for believing the child is in need of aid.
[18]  As with the vagueness issue, the father did not raise this issue below, and thus we review the question for plain error. L.A.M., 727 P.2d at 1059.
[19]  The father also argues that it was error for the judge not to tell him he could have an attorney until after he had ruled on the emergency temporary custody petition. The statute requires this hearing to take place within 48 hours of the emergency custody, AS 47.10.142(d). In balancing the parents' and child's rights, the legislature obviously decided that speedy judicial review was the utmost concern, and it was undoubtedly aware that before this first hearing, the parties may not have consulted counsel. The court told the father that he would be provided with appointed counsel from that point on, and also told him his attorney could request a hearing as soon as he wished. We conclude that this procedure does not deprive parents of their due process rights.
