We investigate the completeness of Hoare Logic on the propositional level. In particular, the expressiveness requirements of Cook's proof are characterized propositionally. We give a completeness result for Propositional Hoare Logic (PHL): all relationally valid rules {b1}p1{c1}, ..., {bn}pn{cn} --------------------------- {b}p{c} are derivable in PHL, provided the propositional expressiveness conditions are met. Moreover, if the programs pi in the premises are atomic, no expressiveness assumptions are needed.