In aerodynamic and machine structures, one of the effective ways of dissipating unwanted vibration or noise is to exploit the occurrence of slip at the interface of structural laminates where such members are held together in a pressurised environment. The analysis and experimental investigation of such laminates have established that when subjected to either static or dynamic loading, non-uniformity in interface pressure can have significant effect on both the energy dissipation and the logarithmic damping decrement associated with the mechanism of slip damping. Such behaviour can in fact be effectively exploited to increase the level of damping available in such a mechanism. What has however not been examined is to what extent is the energy dissipation affected by the relative sizes or the material properties of the upper and lower laminates? In this paper the analysis is extended to incorporate such effects. In particular, by invoking operational methods, it is shown that variation in laminate thickness may provide less efficacious means of maximizing energy dissipation than varying the choice of laminate materials but that either of these effects can in fact dwarf those associated with non-uniformity in interface pressure. To achieve this, a special configuration is required for the relative sizes and layering of the laminates. In particular, it is shown that for the case of two laminates, the upper laminate is required to be thinner and harder than the lower one. These results provide a basis for the design of such structures.