This paper suggests simple 3- and 4-step estimators for censored quantile regression models with an envelope or a separation restriction on the censoring probability. The estimators are theoretically attractive (asymptotically as efficient as the celebrated Powell's censored least absolute deviation estimator). At the same time, they are conceptually simple and have trivial computational expenses. They are especially useful in samples of small size or models with many regressors, with desirable finite sample properties and small bias. The envelope restriction costs a small reduction of generality relative to the canonical censored regression quantile model, yet its main plausible features remain intact. The estimator can also be used to estimate a large class of traditional models, including normal Amemiya-Tobin model and many accelerated failure and proportional hazard models. The main empirical example involves a very large data-set on extramarital affairs, with high 68 percent censoring. We estimate 45-90 percent conditional quantiles. Effects of covariates are not representable as location-shifts. Less religious women, with fewer children, and higher status, tend to engage into the matters relatively more than their opposites, especially at the extremes. Marriage longevity effect is positive at moderately high quantiles and negative at high quantiles. Education and marriage happiness effects are negative, especially at the extremes. We also briefly consider the survival quantile regression on the Stanford heart transplant data. We estimate the age and prior surgery effects across survival quantiles. Keywords: Quantile regression, median regression, censoring, duration, survival, classification, discriminant analysis. JEL Classifications: C14, C24, C41, C51, D13.