
313 A.2d 642 (1974)
Grace T. MASSE
v.
Arthur H. MASSE.
No. 1906-Appeal.
Supreme Court of Rhode Island.
January 11, 1974.
*643 Gerald J. Pouliot, for petitioner-appellee.
Varone & McKinnon, Daniel V. McKinnon, Providence, for respondent-appellant.


*644 OPINION
JOSLIN, Justice.
This domestic relations matter is here on a divorced husband's appeal from a Family Court order denying his motion to modify, nunc pro tune, the alimony and child support provisions of the final decree of divorce; finding him in arrears in the amount of $1900 on the payments due thereunder; adjudging him in contempt; and ordering him to pay the arrearages at the rate of $10 a week.
There is no real dispute about the facts. On September 4, 1957, the wife commenced divorce proceedings against her husband and on April 30, 1958, a final decree was entered granting her an absolute divorce, awarding her custody of the minor child of the parties, and ordering the husband to pay her $15 a week for alimony and $17.50 for the support of the child.
On May 9, 1958, the parties executed a writing which purports to be an agreement. It provides in substance that the final decree's alimony and support provisions would be deemed satisfied if the husband paid the wife $32.50 per week while employed and $17.50 per week while collecting Social Security or unemployment compensation payments.[1] For undisclosed reasons, the agreement was not submitted to the Family Court for its approval and the final decree of divorce was not modified.
Thirteen and a half years later, the husband, by then remarried, petitioned the Family Court to reduce the alimony and child support payments provided for in the divorce decree on the ground that a substantial increase in his living expenses had not been matched by a corresponding increase in his income. Thereupon, the wife filed a "cross-complaint" objecting to the requested modification, and asking that the husband be held in contempt for being in arrears in an amount in excess of $1900 on account of the alimony and support payments due under the divorce decree.
The husband in turn filed a "motion to amend judgment nunc pro tunc." He admitted in that motion that he had not made the alimony and support payments required by the final decree, but he nonetheless alleged that he had made those provided for in the 1958 agreement with his wife, and he asked that the final decree be modified retroactively so as to conform with that agreement.
This was the frame of reference in which the trial justice, after hearing the testimony, found that there was no specific evidence which pinpointed when the husband was either employed or out of work and when he had drawn unemployment compensation or Social Security benefits. Hence, the trial justice concluded that the 1958 agreement between the parties, irrespective of whether or not it might under other circumstances be entitled to legal effect, never became operative.
That conclusion, in our judgment, is premised on much too narrow a view of the evidence. True, the record, as the trial justice observed, does not identify with specificity either the days when the husband was employed or those when he was entitled to either unemployment or Social Security payments, but it does include the husband's unequivocal assertion, as well as the wife's acquiescence therein, that he had fully complied with his obligations under the 1958 agreement.
That positive and uncontroverted testimony, though not inherently improbable, self-contradictory, lacking in credence, *645 or unworthy of belief, was completely ignored by the trial justice. This oversight deprives his factual determinations of the great weight to which they might otherwise be entitled, Menard v. Menard, 106 R.I. 709, 712-13, 263 A.2d 98, 100 (1970); Sundlun v. Sundlun, 103 R.I. 25, 32-33, 234 A.2d 358, 363 (1967); and it requires us to accept that testimony as conclusive, Peloso v. Peloso, Inc., 107 R.I. 365, 370, 267 A.2d 717, 720 (1970); Laganiere v. Bonte Spinning Co., 103 R.I. 191, 194-95, 236 A.2d 256, 257-58 (1967); Michaud v. Michaud, 98 R.I. 95, 200 A.2d 6 (1964).
On the record thus viewed it might appear at first blush that this case fits into that category of cases where a husband, acting solely on his own and without the acquiescence or agreement of his former spouse, pays her something less than the amount directed by a divorce decree. In that situation the rule is that each accrued installment of alimony or child support which is allowed to go unpaid becomes a judgment which the courts are thereafter powerless to modify, suspend or vacate. Klimasewski v. Klimasewski, 91 R.I. 308, 162 A.2d 549 (1960); Ciallella v. Ciallella, 81 R.I. 320, 103 A.2d 77 (1954); Parenti v. Parenti, 71 R.I. 18, 41 A.2d 313 (1945).
But this is not that kind of case. Here, on the present record, the question is not whether the alimony and child support provisions of a final divorce decree can be retroactively modified, but whether an agreement entered into subsequent to final decree, to the extent that it is fully satisfied, is available to the husband as a bar to his former wife's attempt to recover the unpaid portions of alimony and child support allowances which accrued under that decree.
The result of making such an agreement so available, to be sure, will be no different from what it would be were the decree modified as to past due installments of alimony and child support. It will have been achieved, however, not by the modification process, but by application of principles of the law of contracts, or by virtue of estopping the wife from recovering anything in addition to what she agreed to accept more than 15 years ago in complete satisfaction of her former husband's family obligations. The parties were then sui juris, apparently dealing at arm's length and, though once husband and wife, were then and are now divorced.
Certainly their agreement, at least to the extent it touched future alimony payments, would have been recognized and enforced if it had been presented to the Family Court for approval and if it appeared to that court that its terms were fair and reasonable to the parties and not collusive. Reynolds v. Reynolds, 53 R.I. 326, 166 A. 686 (1933); Brown v. Brown, 48 R.I. 420, 138 A. 179 (1927); Ward v. Ward, 48 R.I. 60, 135 A. 241 (1926).
On principle we can perceive no sound reason why that agreement, if fair and otherwise valid, should not be similarly recognized with respect to past due installments of alimony. The argument against such recognition, as we have already observed, is that those installments had ripened into judgments and could not therefore be satisfied by the payment, or promise of payment, of lesser sums. But that argument takes no account of those general principles of the law of contracts which say that a judgment is a proper subject matter for a release or an accord and satisfaction[2] which will bind the parties if fully complied with and supported by sufficient consideration. Little Rock Packing Co. v. Massachusetts Bonding & Ins. Co., 262 F.2d 327 (8th Cir.1959); cf. Erwin *646 v. Erwin, 251 Iowa 1344, 1349, 105 N.W.2d 489, 493 (1960).
Other courts have reached a like conclusion, although relying to some extent on varying rationales. Luedke v. Behringer, 143 So.2d 218 (Fla. Dist. Ct. App. 1962); Montgomery v. Montgomery, 309 S.W.2d 188 (Ky. 1958); Maxey v. Maxey, 212 S.W.2d 810 (Kansas City, Mo., Ct. App. 1948) (estoppel); Hill v. Hill, 106 Colo. 492, 107 P.2d 597 (1940); Dutcher v. Dutcher, 103 Kan. 645, 175 P. 975 (1918); see Feves v. Feves, 198 Ore. 151, 254 P.2d 694 (1953). Contra, Marks v. Marks, 98 Utah 400, 404, 100 P.2d 207, 209 (1940); but see Wallis v. Wallis, 9 Utah 2d 237, 342 P.2d 103 (1959).
Insofar as the agreement before us may affect past due child support payments[3] its recognition and enforcement stand on a different footing from those of past due alimony. This is so because no agreement between the divorced parties can deprive the Family Court of its jurisdiction over the support of their children. Reynolds, supra at 329, 166 A. at 688. Thus, the court to which this agreement may be presented should, as a condition to its recognition, be satisfied (1) that it meets the same requirements as those set forth above with respect to arrearages for alimony, and (2) that it has related the child's needs and welfare to the father's ability to provide therefor. Heatherton v. Heatherton, 110 R.I. 144, 290 A.2d 912 (1972); see Anthony v. Anthony, Iowa, 204 N.W.2d 829 (1973) (agreement enforced if in child's best interest).
Since this case must, in any event, be remanded to the Family Court for further proceedings consistent with this opinion, that court should then make an initial determination of whether this particular agreements is certain and explicit enough to be enforced.
The respondent-husband's appeal is sustained, the decree appealed from is reversed, and the case is remitted to the Family Court for further proceedings consistent herewith.
ROBERTS, C. J., did not participate.
NOTES
[1]  The agreement reads: "May 9, 1958. We, Arthur and Grace Masse, have agreed by mutual consent, that Arthur will not be declared in the arrears on his payments of Alimony and Support for Grace and Lori Masse, as of the following terms for payments.

$17.50 per week when Arthur is collecting Social Security or unemployment.
$32.50 per week when Arthur is working at his place of employment.
                         Signed Grace T. Masse
                         Signed Arthur H. Masse
                         Witness Dorothy C. Masse."

[2]  General Laws 1956 (1969 Reenactment) § 9-21-2 in pertinent part provides:

"On motion and upon such terms as are just, a court may relieve a party or his legal representative from a final judgment, order, decree, or proceeding entered therein for the following reasons: * * * (5) the judgment has been satisfied, released or discharged * * *."
[3]  The fact that the 1958 document provides for a $17.50 weekly payment during periods of unemployment may suggest that the parties did not intend to vary the child support order. In the first instance, however, this is for the trial justice to determine.
