In Information Retrieval (IR), the Dirichlet Priors have been applied to the smoothing technique of the language modeling approach. In this paper, we apply the Dirichlet Priors to the term frequency normalisation of the classical BM25 probabilistic model and the Divergence from Randomness PL2 model. The contributions of this paper are twofold. First, through extensive experiments on four TREC collections, we show that the newly generated models, to which the Dirichlet Priors normalisation is applied, provide robust and effective performance. Second, we propose a novel theoreticallydriven approach to the automatic parameter tuning of the Dirichlet Priors normalisation. Experiments show that this tuning approach optimises the retrieval performance of the newly generated Dirichlet Priors-based weighting models. Categories and Subject Descriptors H.3.3 [Information Storage and Retrieval]: Retrieval models General Terms Experimentation, Performance, Theory Keywords Term frequency normalis...