Compositional static analysis has enabled the application of bug-finding techniques at scale, as demonstrated by tools such as Infer’s Pulse engine. However, restricting the analysis to the level of procedures results in losing awareness of the program state when a function is called. In particular for procedures involving dynamic dispatching or argument pointer aliasing, context is essential for effective specification inference. This work presents \emph{specialisation}, a mechanism that enables the generation of summaries tailored to individual call site contexts when necessary. We discuss the intuition behind our formalisation of this technique and present our preliminary results on the impact of specialisation when analysing open-source projects with the Pulse engine.