In this paper we consider three well-known procedures of unequal probability sampling without replacement. Using an asymptotic approach, Hartley and Rao [3] have obtained compact expressions for variance and estimated variance for one of these procedures. Here we develop formulae for variance and estimated variance for the other two procedures, using their asymptotic approach. It is shown that for large and moderate size populations the three procedures have almost the same variance so that there is little to choose between the three procedures on the basis of variance alone. Therefore, some discussion of other factors for choosing between the three procedures is given.