Monte Carlo studies of several fixed-effects methods for combining and comparing correlation matrices have shown that two refinements improve estimation and inference substantially. With rare exception, however, these simulations have involved homogeneous data analyzed using conditional meta-analytic procedures. The present study builds on previous evidence about these methods' relative performance by examining their behavior under heterogeneity, which is more realistic in practice. Results based on both conditional and unconditional estimands indicate that of the two refinements, using estimated correlations in conditional (co)variances improves point and interval estimates of mean correlations more than analyzing Fisher Z correlations, despite the latter's superiority for testing homogeneity. Recommended choices among methods are offered. (Contains 4 notes, 2 tables, and 7 figures.)