This note is concerned with estimating censored quantile regressions (CQR). As its major contribution, a' new algorithm, called BRCENS, is developed as an adaption of the Barrodale-Roberts algorithm for the standard quantile regression problem. In a subsequent simulation study, BRCENS performs well in comparison with the iterative linear programming algorithm (ILPA) suggested recently by Buchinsky. In the theoretical analysis, this note generalizes the asymptotic theory for estimating CQR to the case with observation specific censoring points and with fairly arbitrary non-stationarity and dependency in the data. Building on the interpolation property of the coefficient estimate, the ILPA is shown to suffer from some theoretical inconsistencies.