identically distributed location points, however considering only jumps larger than a threshold ε. Therefore, the number of jumps of the new process, called ε-NGG process, is a.s. finite. A prior distribution for ε can be elicited. We will assume such a process as the mixing measure in a mixture model for density and cluster estimation. We also build an efficient Gibbs sampler scheme to simulate from the posterior. Finally, the performance of our model on two popular datasets will be illustrated.