Kappa is a language geared towards the modelling of the complex systems of reactions that can occur between proteins inside cells. It is supported by sophisticated simulation and static analysis techniques which can be applied to the models to study their emergent behaviour. Part of this is the construction by the simulator of causal histories explaining the generation of patterns of connectivity that the user speci es to be of interest, for example the existence of links between speci ed kinds of protein. Standard notions of independence of rule applications fail to provide adequately concise causal histories, leading to the earlier formulation of strong and weak forms of trajectory compression for Kappa. In this paper, we give a simple categorical account of how forms of compression can be uniformly obtained. This generalisation also describes a way for the user to specify their own levels of compression between weak and strong, which we call ltered compression. This is based on the idea of the user specifying the part of the type graph that represents the the structure which the compression technique should track through the trace.