We introduce a simple and efficient sampling strategy for the Dirichlet Process Mixture model (DPM) and its two-parameter extension, the Poisson-Dirichlet process mixture model, also known as the Pitman-Yor process Mixture model (PYM). Inference in DPM and PYM is usually performed using Markov Chain Monte Carlo (MCMC) methods, specifically the Gibbs sampler. These sampling methods are usually divided into two classes: marginal and conditional algorithms. Each method has its own merits and limitations. The aim of this paper is to propose a simple and effective strategy that combines the main advantages of each class. Extensive experiments on simulated and real data highlight that the proposed sampler is relevant and performs much better than its competitors.