Earlier work showed how to perform fixed-effects meta-analysis of studies or trials when each provides results on more than one outcome per patient and these multiple outcomes are correlated. That fixed-effects generalized-least-squares approach analyzes the multiple outcomes jointly within a single model, and it can include covariates, such as duration of therapy or quality of trial, that may explain observed heterogeneity of results among the trials. Sometimes the covariates explain all the heterogeneity, and the fixed-effects regression model is appropriate. However, unexplained heterogeneity may often remain, even after taking into account known or suspected covariates. Because fixed-effects models do not make allowance for this remaining unexplained heterogeneity, the potential exists for bias in estimated coefficients, standard errors and p-values. We propose two random-effects approaches for the regression meta-analysis of multiple correlated outcomes. We compare their use with fixed-effects models and with separate-outcomes models in a meta-analysis of periodontal clinical trials. A simulation study shows the advantages of the random-effects approach. These methods also facilitate meta-analysis of trials that compare more than two treatments.