We propose a classical Laplace estimator alternative for a large class of -consistent estimators, including isotonic regression, monotone hazard, and maximum score estimators. The proposed alternative provides a unified method of smoothing; easier computation is a byproduct in the maximum score case. Depending on input parameter choice and smoothness, the convergence rate of our estimator varies between and (almost) and its limit distribution varies from Chernoff to normal. We provide a bias reduction method and an inference procedure which automatically adapts to the correct convergence rate and limit distribution.