Approximate solution of the differential equations of state of continuous systems by various numerical integration schemes is standard practice in trajectory optimization and control work; the resulting truncation error represents the main error in many applications. Suppression of the deleterious effects of this error is of increasing interest as double-precision arithmetic becomes routinely available for roundoff error reduction, especially when high overall accuracy is needed. In numerical optimization of trajectories, the accuracy of partial derivatives is important in a special sense: compatibility of a function and its derivatives. That is, if the partial derivatives of the terminal state with respect to trajectory parameters are accurate representations of the partial derivatives of the terminal state calculated through the integration model, adverse effects on convergence of successive approximation iterations can be avoided. From previous numerical experiments, this is known to be particularly important when conjugate-direction methods are used, as they require unusually accurate first partial derivatives to realize the quadratic convergence theoretically attainable.