We study algorithms for computing stable models of logic programs andderive estimates on their worst-case performance that areasymptotically better than the trivial bound of $O(m 2^n)$, where $m$ is the size of an input programand $n$ is the numberof its atoms. For instance, for programs whose clauses consist of atmost two literals (counting the head) we design an algorithm tocompute stable models that works in time $O(m\times 1.44225^n)$. We present similarresults for several broader classes of programs. Finally, we studythe applicability of the techniques developed in the paper to theanalysis of the performance of smodels.