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We consider the problem of assessing whether an exposure affects a dichotomous outcome other than by modifying a given mediator. The standard approach, logistic regression adjusting for both exposure and the mediator, is known to be biased in the presence of confounders for the mediator-outcome relationship. Because additional regression adjustment for such confounders is only justified when they are not affected by the exposure, inverse probability weighting has been advocated, but is not ideally tailored to mediators that are continuous or have strong measured pre-dictors. We overcome this limitation by developing inference for a novel class of causal models that are closely related to Robins ’ logistic structural direct effect models, but do not inherit their diffi-culties of estimation. We study identification and efficient estimation under the assumption that all confounders for the exposure-outcome and mediator-outcome relationships have been measured, and find adequate performance in simulation studies. We discuss extensions to case-control studies and relevant implications for the generic problem of adjustment for time-varying confounding