This paper deals with the problem of finding the K smallest elements out of a totally ordered but non-sorted set of N elements. This problem, called K-selection, arises often in statistics, image processing and distributed computing. We propose two algorithms to solve this problem in hypercubes. Our first algorithm is asymptotically optimal when K = O(( N)β), for any constant β. The second enlarges the range of optimality to K = N∊, ∊ < 1, using a recursive strategy. These are major improvements on previous results.