The Model Parameter Randomisation Test (MPRT) is widely acknowledged in the eXplainable Artificial Intelligence (XAI) community for its well-motivated evaluative principle: that the explanation function should be sensitive to changes in the parameters of the model function. However, recent works have identified several methodological caveats for the empirical interpretation of MPRT. In this work, we introduce two adaptations to the original MPRT---Smooth MPRT and Efficient MPRT, where the former minimises the impact that noise has on the evaluation results and the latter circumvents the need for biased similarity measurements by re-interpreting the test through the explanation's rise in complexity, post-model randomisation. Our experimental results demonstrate improved metric reliability, for more trustworthy applications of XAI methods.