Prodigy 4.0's planning algorithm uses domain-independent search heuristics. In this paper, we support our belief that there is no single search heuristic that performs more efficiently than others for all problems or in all domains. The paper presents three different domain-independent search heuristics of increasing complexity. We run Prodigy 4.0 with these heuristics in a series of artificial domains (introduced in [Barrett and Weld 93]) where in fact one of the heuristics performs more efficiently than the others. However, we introduce an additional simple domain where the apparently worst heuristic outperforms the other two. The results we obtained in our empirical experiments lead to the main conclusion of this paper: planning algorithms need to use different search heuristics in different domains. We conclude the paper by advocating the need to learn the correspondence between particular domain characteristics and specific search heuristics for planning efficiently in complex domains.