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In randomized experiments, adjusting for observed features when estimating treatment effects has been proposed as a way to improve asymptotic efficiency. However, only linear regression has been proven to form an estimate of the average treatment effect that is asymptotically no less efficient than the treated-minus-control difference in means regardless of the true data generating process. Randomized treatment assignment provides this "do-no-harm" property, with neither truth of a linear model nor a generative model for the outcomes being required. We present a general calibration method which confers the same no-harm property onto estimators leveraging a broad class of nonlinear models. This recovers the usual regression-adjusted estimator when ordinary least squares is used, and further provides non-inferior treatment effect estimators using methods such as logistic and Poisson regression. The resulting estimators are non-inferior to both the difference in means estimator and to treatment effect estimators that have not undergone calibration. We show that our estimator is asymptotically equivalent to an inverse probability weighted estimator using a logit link with predicted potential outcomes as covariates. In a simulation study, we demonstrate that common nonlinear estimators without our calibration procedure may perform markedly worse than both the calibrated estimator and the unadjusted difference in means.