Prime implicants/implicates (PIs) have been shown to be a useful tool in several problem domains. In model-based diagnosis (MBD), de Kleer et al. (Proc. AAAI-90) have used PIs to characterize diagnoses. We present a PI generation algorithm which, although based on thegeneral SE-tree-based search framework, is effectively an improvement of aparticular PI generation algorithm proposed by Slagle et al. (IEEE Trans. Comput. 19(4) (1970)). The improvement is achieved via adecomposition tactic which is boosted by the SE-tree-based framework. The new algorithm is also more flexible in a number of ways. We present empirical results comparing the new algorithm to the old one, as well as to current PI generation algorithms.