An important problem in automatic parallelization of scientific programs is to generate loops from an algebraic description of the iteration domain. The usual technique is to produce a perfectly nested set of loops, whose bounds consist in maxima and minima of several affine functions. However, perfect loop nests suffer from the run-time overhead of evaluating bound expressions and do not allow to scannon-convex domains efficiently. In this paper we study a candidate loop structure for overcoming these problems. This structure, called nested loop sequence (NLS) is defined as a sequence of DO loops whose bodies are nonempty sequences of DO loops. We propose an algorithm to compute a NLS scanning a given convex polyhedron, which overcomes the run-time overhead problem. The algorithm produces a loop structure in which the bounds of every loop consist each in a single affine functions.