Let G be a graph with no three independent vertices. How many edges of G can be packed with edge-disjoint copies of Kk? More specifically, let fk(n, m) be the largest integer t such that, for any graph with n vertices, m edges, and independence number 2, at least t edges can be packed with edge-disjoint copies of Kk. Turán's theorem together with Wilson's Theorem assert that if . A conjecture of Erdős states that for all plausible m. For any ε > 0, this conjecture was open even if . Generally, f_k(n,m) may be significantly smaller than . Indeed, for k=7 it is easy to show that for m ≈ 0.3n2. Nevertheless, we prove the following result. For every k≥ 3 there exists γ>0 such that if then . In the special case k=3 we obtain the reasonable bound γ ≥ 10−4. In particular, the above conjecture of Erdős holds whenever G has fewer than 0.2501n2 edges.