Formulations are provided for a partially modified approach to standard generalized estimating equations (GEE) methods for modeling correlated sets of univariate outcomes. This approach allows for non-constant dispersions by combining extra estimating equations for dispersion parameters with standard GEE estimating equations for mean parameters. The extra estimating equations are generated by maximizing an appropriate likelihood function in the dispersion parameters. Generalizations of standard GEE estimates of correlation parameters are provided accounting for non-constant dispersions along with tests for significant mean and dispersion parameter estimates. The special case with constant dispersions is formulated and compared to standard GEE. Possible degeneracy in correlation estimates is addressed. A detailed estimation process is described that limits the impact of estimation problems through extensions of Newton's method. The issue of variation in measurement conditions is addressed as well.