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We investigate, both analitically and numerically, a one dimensional lattice model with next neighbour dissipative but momentum conserving interactions. By using the local equilibrium approximation, hydrodynamic equations are derived, both at the average and the fluctuating level of approach. Interestingly, we find deviations from Haff's law in the homogeneous cooling state, stemming from velocity correlations, and a plausible physical explanation is provided. Moreover, a very good agreement between simulations and theory has been found. |