Observational equivalences can be used to reason about the correctness of security protocols described in the spi-calculus. Unlike in CCS or in Π-calculus, these equivalences do not enjoy a simple formulation in spi-calculus. The present paper aims at enriching the set of tools for reasoning on processes by providing a few equational laws for a sensible notion of spi-bisimilarity. We discuss the dificulties underlying compositional reasoning in spi-calculus and show that, in some cases and with some care, the proposed laws can be used to build compositional proofs. A selection of these laws forms the basis of a proof system that we show to be sound and complete for the strong version of bisimilarity.