Let G be an undirected graph and let Γ be its drawing on a plane. Each vertex in G has a label with a specified size. In this paper, we consider the problem of placing the maximum number of vertex labels in Γ in such a way that they do not overlap any vertices, edges or other labels. By refining several portions of the Kakoulis-Tollis algorithm for labeling graphical features, we present a heuristic algorithm for this problem. Experimental results show that our algorithm can place more labels than previous algorithms.