The present paper is an exploratory investigation to overcome difficulties encountered in the simulation of dense granulates when a NSCD approach is used. Some simple examples permit identification of impulse indetermination as the main cause of the failure or the slowdown of the numerical algorithm. We propose to deal directly with the space of impulses with null resulting momentum. A prediction-correction scheme is detailed and enriched to restrict at best the interpenetration. Finally sophisticated tools are developed to preserve the sparsity of the matrices and consequently to ensure an efficient implementation of an adapted nonsmooth solver.