A population ofNunits is considered. It is assumed that each unit has a “size measure,”pi, associated with it (Σpi= 1). A sample ofnunits is to be selected one by one without replacement and in such a way that the probability for thei-th unit to be in the sample isnpi.To achieve this a method is proposed whereby the probability for thei-th unit to be selected is equal topiat each of thensuccessive selections. The procedure may be applied to one-stage sampling or to multi-stage sampling. In the latter case a self-weighting estimator is supplied, which is applicable even in the case where the sample at subsequent surveys is partially replaced (“rotating sample”).