We study the following problem: given a biological sequence S, a multiset Click to view the MathML source of motifs and an integer k, generate uniformly random sequences which contain the given motifs and have exactly the same frequencies of occurrence of k-lets (i.e. factors of length k) of S. We notably prove that the problem of deciding whether a sequence respects the given motif constraints is NP-complete. Nevertheless, we give a random generation algorithm which turns out to be experimentally efficient.