The effects, in terms of bias and precision, of omitting non-confounding predictive covariates from generalized linear models have been well studied, and it is known that such omission results in attenuation bias but increased precision with logistic regression. However, many epidemiologic risk analyses utilize alternative models that are not based on a linear predictor, and the effect of omitting non-confounding predictive covariates from such models has not been characterized. We employed simulation to study the effects on risk estimation of omitting non-confounding predictive covariates from an excess relative risk (ERR) model and a general additive-multiplicative relative-risk mixture model for binary outcome data in a case-control setting. We also compared the results to the effects with ordinary logistic regression. For these commonly employed alternative relative-risk models, the bias was similar to that with logistic regression when the risk was small. More generally, the bias and standard error of the risk-parameter estimates demonstrated patterns that are similar to those with logistic regression, but with greater magnitude depending on the true value of the risk. The magnitude of bias and standard error had little relation to study size or underlying disease prevalence. Prior conclusions regarding omitted covariates in logistic regression models can be qualitatively applied to the ERR and the general additive-multiplicative relative-risk mixture model without substantial change. Quantitatively, however, these alternative models may have slightly greater omitted-covariate bias, depending on the magnitude of the true risk being estimated.