Coefficient omega indices are model-based composite reliability estimates that have become increasingly popular. A coefficient omega index estimates how reliably an observed composite score measures a target construct as represented by a factor in a factor-analysis model; as such, the accuracy of omega estimates is likely to depend on correct model specification. The current paper presents a simulation study to investigate the performance of omega-unidimensional (based on the parameters of a one-factor model) and omega-hierarchical (based on a bifactor model) under correct and incorrect model misspecification for high and low reliability composites and different scale lengths. Our results show that coefficient omega estimates are unbiased when calculated from the parameter estimates of a properly specified model. However, omega-unidimensional produced positively biased estimates when the population model was characterized by unmodeled error correlations or multidimensionality, whereas omega-hierarchical was only slightly biased when the population model was either a one-factor model with correlated errors or a higher-order model. These biases were higher when population reliability was lower and increased with scale length. Researchers should carefully evaluate the feasibility of a one-factor model before estimating and reporting omega-unidimensional.