Summary: In the censored regression model, some regression estimators are introduced using weighted integrals of the log-rank estimating functions. Their limiting covariance matrices do not involve the error density and can be reliably estimated. Inference can then be easily obtained. Some of these estimators have high asymptotic efficiency at some important submodels. Some lack-of-fit tests are derived that require little extra computing time. These tests are asymptotically normal under the model and consistent against certain monotone or convex model misspecifications. Numerical studies show that for some weight functions, the estimators and tests perform well. Implementation of the proposed procedures is discussed and illustrated in a real data example.