In this work we explore and evaluate the effect of automatic code specialisation on auto-generated GPU kernels. When combining the high productivity coding environment of computational science with the Just-In-Time compilation nature of many GPU runtime systems there is a clear cut opportunity for code optimisation and specialisation. We have developed a hybrid kernel generation method which is shown to be useful and competitive across very different use cases, and requires minimal knowledge of the overall structure of the program. Stencil codes which are commonly found at the core of computer simulations are ideal candidates for this type of code specialisation. For exactly this type of application we are able to achieve speedups of up to 2.5 times with the implemented strategy.