Even though an active-controlled trial provides no information about placebo, investigators and regulators often wonder how the experimental treatment would compare to placebo should a placebo arm be included in the study. A putative placebo analysis attempts to address this question by combining information from previous studies comparing the active control with placebo. Such an analysis often requires a constancy assumption, namely that the control effect relative to placebo is constant across studies. When the constancy assumption is in doubt, there are ad hoc methods that "discount" the historical data in conservative ways. This paper presents a different approach that does not require constancy or involve discounting, but rather attempts to adjust for any imbalances in covariates between the current and historical studies. This covariate-adjusted approach is valid under a conditional constancy assumption which requires only that the control effect be constant within each subpopulation characterized by the observed covariates. Simulation results show that the proposed method performs reasonably well in moderate-sized samples. The method is illustrated with an example concerning benign prostate hyperplasia.