
523 N.W.2d 755 (1994)
In re the MARRIAGE OF Barbara Ann HARVEY and Charles Newell Harvey.
Upon the Petition of
Barbara Ann Harvey, Appellant,
And Concerning
Charles Newell Harvey, Appellee.
No. 92-1868.
Supreme Court of Iowa.
November 23, 1994.
Garold F. Heslinga of Heslinga, Heslinga & Dixon, Oskaloosa, for appellant.
Scott Campbell of Scott Campbell, P.C., Oskaloosa, for appellee.
Considered by McGIVERIN, C.J., and HARRIS, LARSON, LAVORATO, and SNELL, JJ.
HARRIS, Justice.
We agree with the district court and the court of appeals that, under these special circumstances, the doctrine of equitable estoppel bars a mother from recovering for past child support.
The marriage of petitioner-appellant Barbara Harvey and respondent-appellee Charles Harvey was dissolved in 1986. The dissolution decree awarded the parties joint legal custody of their minor son, Jonathan. *756 Barbara was to have primary physical care. Charles was ordered to pay child support.
Later Barbara remarried. Jonathan did not get along with his stepfather and asked Charles if he could live with him in Houston, Texas. Through her attorney, Barbara agreed to allow Jonathan to do so. Jonathan stayed with Charles, who provided all support during the period from January 1989 to July 1992.
Barbara agreed that Charles would not have to pay child support while Jonathan was with Charles. The parties contemplated that, in exchange for Barbara's agreement to allow Jonathan's move, Charles would not ask her for child support while Charles supported Jonathan in Houston. Barbara however did not agree to a modification of the dissolution decree, promising instead to execute release and satisfaction of judgments periodically.
Although Barbara now claims she allowed Jonathan to spend only six months in Houston, correspondence between the parties' attorneys contains no mention of a six-month period. During Jonathan's stay in Houston, Barbara visited him several times and, contrary to what she now claims, never made any oral or written demands that Jonathan return to Iowa. She never asked the court to order Jonathan's return.
In May of 1992, after Jonathan returned to Iowa, Barbara initiated a garnishment action for the allegedly delinquent child support for the time Jonathan lived in Houston. Contrary to her agreement, Barbara had never filed any satisfaction of judgments while Jonathan was in Houston. The only satisfaction was filed after Barbara's present garnishment action was initiated and it covered only the first six months of the period.
After Charles' objections to garnishment were overruled, he filed an application for modification, alleging the existence of an oral agreement abating his child support obligations for the period when Jonathan lived with him. The district court ordered a reduction of child support in an amount representing the forty-one months Jonathan spent in Houston.
That order did not address the effect of Iowa Code section 598.21(8)(l) (1991).[1] For this reason Barbara petitioned for reconsideration. In an order denying reconsideration, the district court reaffirmed its holding, this time relying on the doctrine of equitable estoppel. The garnishment was quashed. The matter is before us on further review of a court of appeals decision affirming the district court judgment.
I. We agree with Barbara that Code section 598.21(8)(l) overrules Anthony v. Anthony, 204 N.W.2d 829, 831 (Iowa 1973) ("[d]ivorced parents may contract between themselves as to the support of their minor child if the best interest of the child is not injured thereby").
Strong public policy supports the statute. The courts should be loath to sort through numberless disputed claims of undocumented private agreements concerning support obligations. A matter so important should be clearly fixed and authorized by court order. Only in this way can support be effectively enforced. The statute spares the courts from the impossible task of separating fact from fiction in claims of the parties' private understandings. The legislature had every right to void secret agreements that would obviate court ordered support obligations.
II. For this reason also, the doctrine of equitable estoppel should be rarely applied in cases of this kind. We stop just short, however, from saying the doctrine should never be applied. And it seems to us that, if it ever can be, the doctrine should apply to the facts here.
The elements of promissory estoppel (a proper legal theory in cases where the reliance is on a promise rather than a misrepresentation of fact, Merrifield v. Troutner, 269 N.W.2d 136, 137-38 (Iowa 1978)) are:
(1) a clear and definite oral agreement;

*757 (2) proof that plaintiff acted to his detriment in reliance thereon; and
(3) a finding that the equities entitle plaintiff to [the] relief.
Id. at 137 (quoting Johnson v. Pattison, 185 N.W.2d 790, 795 (Iowa 1971)).
Here Charles easily sustained his burden of proving each of these elements. First he established an oral agreement with Barbara (he would not have to pay child support during that period when Jonathan was living with him). Like the trial court, we find Barbara's testimony unconvincing. She had many opportunities to object or to press her right of Jonathan's custody. Her conduct during the period was only consistent with the existence of an agreement with Charles. Secondly Charles acted to his detriment in relying on the oral agreement. Finally the equities strongly favor Charles. He spent over $22,000 in living expenses for Jonathan during the period. If Barbara were to receive child support for that period it would not be for Jonathan but for her. So the elements for equitable estoppel appear.
Because of Iowa Code section 598.21(8)(l), though, it does not follow that equitable estoppel should be applied. A statutory mandate cannot be ignored in the interest of balancing equities among the parties. We nevertheless conclude the statute should not bar the doctrine here because to do so would be inappropriate and at variance with the intent of the legislature. It would in no way further the considerations which prompted the statute's enactment, and would reward the very sort of conduct at which the legislation was aimed.
We cannot believe the legislature intended the statute to apply so as to compensate Barbara for her refusal to perform her agreement to enter satisfactions of the judgment, especially after she promised the satisfactions as an alternative to the modification suggested by Charles. Dwyer v. Clerk of District Court, 404 N.W.2d 167, 171 (Iowa 1987) (requiring clerk to enter satisfactions of judgment for direct, out-of-court, child support payments, notwithstanding statutory requirement that payments be made through court).
We conclude that the trial court correctly rejected Barbara's support claims because they are barred by the doctrine of promissory estoppel. We are impressed by the following facts: (1) the claimed arrearage is for a period during which Charles provided all Jonathan's support; (2) the support Charles provided exceeded the amount of his obligation under the court order; (3) Barbara agreed that the obligations would be satisfied in this manner; and (4) any amount now recovered would not inure for Jonathan's support, but solely for Barbara's benefit.
DECISION OF COURT OF APPEALS AND DISTRICT COURT JUDGMENT AFFIRMED.
NOTES
[1]  That section provides:

A modification of a support order entered under ... this chapter between parties to the order is void unless the modification is approved by the court, after proper notice and opportunity to be heard is given to all parties to the order, and entered as an order of the court.
