In this paper we propose an adjustment based on post-treatment variables for some standard estimators of the average treatment effect on the treated. Under relatively weak conditions, this adjusted estimator will provide an upper bound for the effect and in some cases lower bounds on p-values. Additionally, this approach does not place a restriction on the outcome variable and allows for multiple mechanisms by which the treatment has an effect on the outcome. We also demonstrate that this adjustment will reduce the estimated effect in a wide variety of circumstances, and therefore, when the assumptions for the adjusted estimator are preferable to the assumptions for the unadjusted estimator, the adjustment can be used as a robustness check. This method is illustrated with an assessment of the effects of using plurality rules for the first multi-party presidential elections in third wave of democracy in sub-Saharan Africa.