The spi calculus is an extension of the pi calculus with cryptographic primitives, which was designed for the verification of cryptographic protocols. Because of this extension, the naive adaptation of labelled bisimulations from the pi calculus is too strong to be useful for the purposes of verification. Instead, as a viable alternative, several ‘environment-sensitive’ bisimulations have been proposed. In this paper, we present a formal study of the differences between these bisimulations.