The intensity coherence function of time for partially saturated acoustic propagation through internal waves is calculated with a method that is improved over previous treatments. Two specific improvements are introduced: The usual expansion in (1/ΛΦ2) is carried out to a higher order, and then the terms of that expansion are calculated with a new perturbative method. The method is applied to propagation without a sound channel, for both phase-screen and continuous-medium cases. The validity of the new perturbative method is estimated by calculating the next order error terms. Accuracies at the few-percent level are found. The new analytic formulas are also corroborated with numerical integration. Finally, the method is applied to a specific ocean-acoustic experiment [Azores Fixed Acoustic Range (AFAR)]. In order to achieve good agreement with experiment it will be necessary to add an accurate treatment of the sound channel to the present perturbation method.