Abstract Many computer vision algorithms include a robust estimation step where model parameters are computed from a data set containing a significant proportion of outliers. The ransac algorithm is possibly the most widely used robust estimator in the field of computer vision. In the paper we show that under a broad range of conditions, ransac efficiency is significantly improved if its hypothesis evaluation step is randomized . A new randomized (hypothesis evaluation) version of the ransac algorithm, r-ransac , is introduced. Computational savings are achieved by typically evaluating only a fraction of data points for models contaminated with outliers. The idea is implemented in a two-step evaluation procedure. A mathematically tractable class of statistical preverification test of samples is introduced. For this class of preverification test we derive an approximate relation for the optimal setting of its single parameter. The proposed pre-test is evaluated on both synthetic data and real-world problems and a significant increase in speed is shown.