
819 So.2d 1108 (2002)
Henry S. CASEY
v.
Alpha Webb CASEY.
No. 2002-CA-0246.
Court of Appeal of Louisiana, Fourth Circuit.
May 22, 2002.
*1110 J. Browne Larose, III, New Orleans, LA, for Plaintiff/Appellee.
Harry F. Connick, District Attorney, Elizabeth D. Chatelain, Assistant District Attorney, New Orleans, LA, for Defendant/Appellant.
(Court composed of Judge JOAN BERNARD ARMSTRONG, Judge MIRIAM G. WALTZER, Judge DENNIS R. BAGNERIS, SR.).
Judge MIRIAM G. WALTZER.
The State, seeking enforcement of a consent judgment awarding child support, filed a motion for contempt and arrearages. The trial court awarded arrearages to the obligee, Alpha Casey, against Henry Casey, the obligor, but reduced the amount owed for the time period for which Henry Casey was incarcerated but had not filed a motion to reduce or modify the award. The State appeals arguing that the trial court erred in reducing the amount of the obligation for the period of the obligor's incarceration, since this period pre-dated judicial demand.

STATEMENT OF FACTS AND HISTORY OF THE CASE
On 11 August 1995 Henry Casey sued for divorce from Alpha Casey. On 7 September 1995 Alpha Casey filed a rule for child support and alimony. On 28 March 1996 the trial court signed a judgment of divorce. On 9 July 1996 the parties confected a consent judgment. Specifically, Henry Casey agreed to pay $1,500.00 per month in child support for the couple's three minor children, to provide medical insurance for the three children, and to pay 80% of the uncovered medical and dental expenses. Furthermore, the judgment provided, "Alpha Casey's claims for additional child support for the private school tuition and summer camp expenses be and the same are hereby reserved pending compromise by the parties or the resetting for trial by this court." Sometime after this consent judgment, the oldest daughter reached majority and the parties agreed among themselves to reduce the monthly obligation to $1,000.00.
From February 1999 until April 2000, Henry Casey was incarcerated and unemployed but he did not seek a modification or reduction of his child support obligation. During his incarceration, Henry Casey continued to pay the children's school tuition and expenses, totaling $13,000.00. The parties do not contest the amount paid by Henry Casey for the children's expenses during his incarceration.
On 11 August 2000, the State sought enforcement of the consent judgment by requesting an immediate garnishment of Henry Casey's income. On 4 October 2000 the State filed a rule to establish arrears, for contempt and to make the past due support executory. On 3 November 2000 Henry Casey moved to modify support and custody. Henry Casey demanded that the court reduce his child support obligation. On 27 November 2001 the parties entered *1111 into a second consent judgment in which Henry Casey agreed to modify the amount owed for child support to $618.00 per month and to pay an amount of $122.00 per month for arrears. Moreover, the parties agreed that Henry Casey was entitled to a credit against the amount of arrears totaling $2,524.00 for the period of time in which the children lived with him. Furthermore, on 27 November 2001 the trial court entered a judgment finding Henry Casey owed arrears totaling $9,088.00, finding that he owed only $1,088 for the period of his incarceration, that he owed $4,000 for the period from May 2000 until August 2000,[1] and that he owed $4,000 for the period from July 2001 until October 2001. The trial court reduced Henry Casey's obligation from $1,000.00 per month to $68.00 per month retroactively for the period of his incarceration, from February 1999 to April 2000.
The State appeals arguing that the trial court erred in reducing the child support obligation for the period of Henry Casey's incarceration, since Henry Casey did not seek such a modification until November 2000. Moreover, the State argues that the trial court erred in failing to find Henry Casey in contempt, and not awarding sanctions and attorneys' fees. This appeal concerns only the trial court's calculation of the arrearages for the period of his incarceration and the failure to find Henry Casey in contempt.
FIRST ASSIGNMENT OF ERROR: The trial court erred in reducing Henry Casey's obligation to pay child support under the judgment for the period of his incarceration, thus reducing the amount of arrears.
The State appeals the award of arrearages arguing that the trial court erred in reducing the amount owed for the period of Henry Casey's incarceration. In 1996, the trial court entered a consent judgment in which Henry Casey agreed to pay $1,500.00 per month in child support, and the parties mutually agreed to reduce this amount to $1,000.00 per month when their oldest child reached majority. From February 1999 until April 2000, Henry Casey was incarcerated and unemployed, but he did not seek reduction of his child support obligation and continued to pay the children's tuition. Only after the State sought arrearages did Henry Casey seek a reduction in his obligation for period of time for which he was incarcerated.
LSA-R.S. 9:315.21 provides, in pertinent part,
C. Except for good cause shown, a judgment modifying or revoking a final child support judgment shall be retroactive to the date of judicial demand.[2]
(Emphasis added.)
We can find no legal basis, and the obligor appears to concede this argument, for modifying the child support award prior to the date of judicial demand. We believe the law is clear that modifications of awards of child support are generally retroactive to the date of judicial demand, except for good cause shown and are then retroactive only to a date subsequent to judicial demand. State Through Department of Health and Human Resources in the Interest of Lymuel v. Duvigneaud, 97-0988 (La.App. 4 Cir. 12/10/97), 704 So.2d 398. We can find no authority for modifying a child support award retroactive to a date prior to judicial demand.
*1112 Alternatively, Henry Casey argues that the trial court's judgment should be affirmed, since the parties agreed to suspend his obligation during his incarceration. However, the trial court did not find that the parties made such an agreement, and Alpha Casey denies that she agreed to suspend the obligation. A child support award may not be modified or terminated unless: (1) proper suit is brought; (2) by operation of law; or (3) the parties enter into a conventional obligation suspending the support award. Jones v. Jones, 99-35 p. 4 (La.App. 3 Cir. 7/14/99), 747 So.2d 94, 96.
Since the parent's duty of support and upbringing is a legal duty owed to a child, it cannot be renounced or suspended. However, the parents may agree to suspend the right to compel collection of this obligation. An essential prerequisite to such a conventional modification of a parent's right to receive support payments is implied. The parent may not, by suspension of this right, thwart the purpose for which the right is established, i.e., the enforcement of the child's right to support and upbringing. An agreement by a parent to suspend his right to receive child support payments will not be enforced unless it meets the requisites for a conventional obligation and fosters the continued support and upbringing of the child. To allow the obligee to suspend his right to receive support payments under circumstances contrary to the child's interests would be inimical to the ultimate goal of support and upbringing of the child. On the other hand, if the parties clearly agree to a suspension of the payments, and such an agreement does not interrupt the child's maintenance or upbringing or otherwise work to his detriment, the agreement should be enforceable. New v. New, 93-702 p. 6 (La.App. 5 Cir. 1/25/94), 631 So.2d 1183, 1186, quoting Dubroc v. Dubroc, 388 So.2d 377 (La.1980). To enforce an extra-judicial agreement modifying a court order of support, the party alleging the agreement must prove that the parties clearly agreed to the modification. New, supra at 93-702 p. 7, 631 So.2d 1183, 1186. The agreement must be specific. Id. Failure to protest or to acquiesce in a unilateral reduction does not defeat an action for arrearages or amount to a waiver. New, supra at 93-702 p. 7, 631 So.2d at 1186, citing Dubroc, supra.
Henry Casey argues that he and his exwife agreed to suspend his obligation to pay child support during his incarceration or that they agreed to substitute his obligation to pay child support with payments for private school tuition. Henry Casey testified that he called his wife from prison and they agreed that his payments for the children's school expenses and tuition would satisfy his obligation under the judgment to pay child support. However, Alpha Casey testified that Henry Casey called from prison and told her that he would continue to pay the children's tuition and school expenses during his incarceration. We do not believe Henry Casey offered sufficient evidence of a specific agreement to suspend Alpha Casey's right to collect support during his incarceration.
Henry Casey argues, in the alternative, that the amount of arrearages should be reduced by the amount he paid for tuition and school expenses. Except under a few exceptional circumstances, child support is satisfied only by payment to the parent to whom it is due. Payment to third parties will not satisfy that obligation, although the obligor is entitled to credit for payments made directly on behalf of the children and at the request of the obligee. New, supra at 93-702 p. 7, 631 So.2d at 1187, citing Dunn v. Dunn, 546 So.2d 819 (La.App. 5 Cir.1989); Keefe v. Keefe, 559 So.2d 987 (La.App. 5 Cir.1990). The jurisprudence has established beyond doubt that justice or equity does not operate *1113 to nullify or reduce an accumulated support award until the judgment is altered by subsequent judgment or operation of law. New, supra at 93-702 p. 8, 631 So.2d at 1186.
Henry Casey neither paid child support nor sought modification of the order requiring him to pay child support during his incarceration. However, he did continue to pay tuition and school expenses for this period of time. Both Henry Casey and Alpha Casey testified that they discussed arrangements in the beginning of his incarceration. Henry Casey was under no court order to pay tuition and school expenses. The parties do not dispute that Henry Casey paid approximately $13,000 in tuition and school expenses for the benefit of the children and with Alpha Casey's knowledge. The evidence establishes that Henry Casey is entitled to a credit for the amount paid for tuition and school expenses during his incarceration.
SECOND ASSIGNMENT OF ERROR: The trial court erred by failing to find Henry Casey in contempt.
The trial court did not find Henry Casey in contempt of the consent judgment obligating him to pay child support.
LSA-C.C.P. art. 224 provides in pertinent part;
Any of the following acts constitutes a constructive contempt of court:
. . . .
(10) Willful disobedience of any lawful judgment, order, mandate, writ, or process of the court; ..."
Under our jurisprudence interpreting this statute, it must be shown by the party seeking this contempt ruling that the alleged offender willfully disobeyed a direct order of the court prior to the contempt rule, otherwise he should not be held in contempt. New, supra at 93-702, p. 9-10, 631 So.2d at 1188. Willful disobedience is an act or failure to act done intentionally, knowingly and purposefully, without justification. A trial court is vested with great discretion in determining whether a person is to be held in contempt for willful disobedience of a trial court judgment. New, supra at 93-702, p. 10, 631 So.2d at 1188, citing Kirby v. Kirby, 579 So.2d 508, 519 (La.App. 4 Cir.1991).
The State in seeking to enforce the consent judgment introduced evidence that Henry Casey did not comply with the court's order to pay child support. However, the evidence does not persuade us the trial court abused its discretion by failing to find that he disobeyed the judgment willfully or without justification. Henry Casey testified that he was incarcerated from February 1999 until April 2000. Moreover, he testified that he was temporarily employed at various places after his incarceration. Although he did not seek modification of the order, he did continue to pay the children's school expenses during the period of his incarceration. Moreover, he testified that he spoke to his wife about his inability to pay child support. We find no error in the trial court's finding.

CONCLUSION
For the above reasons, we reverse the judgment of the trial court retroactively modifying Henry Casey's obligation to pay $1,000 per month in child support, thus retroactively reducing the amount of arrearages. We find that Henry Casey owed child support under the judgment for the period of his incarceration from February 1999 until April 2000, totaling $15,000.[3] However, Henry Casey is entitled to a credit for the school expenses, totaling *1114 $13,000, which he paid on behalf of the children for this time period, since he paid such expenses with Alpha Casey's consent and knowledge and for the benefit of the children. Moreover, he was under no prior order to pay these expenses. Furthermore, we affirm the trial court's order failing to find Henry Casey in contempt. In all other respects the judgment setting the amount of arrearages is affirmed, since these amounts are not the subject of this appeal.
JUDGMENT REVERSED, IN PART, AND AFFIRMED AS AMENDED.
NOTES
[1]  The children lived with Henry Casey from August 2000 until June 2001. The parties do not contest these awards.
[2]  The parties erroneously argue for application of that section of LSA-R.S. 9:315.21, pertaining to modification of interim child support awards.
[3]  Both the trial court and the parties found that the amount of the arrearages under the judgment totaled $16,000. We believe an error in calculation occurred since the time period clearly includes 15 months at $1,000 per month.
