We extend some rate of convergence results of greedy quantization sequences already investigated in [16]. We show, for a more general class of distributions satisfying a certain control, that the quantization error of these sequences have an n − 1 d rate of convergence and that the distortion mis-match property is satisfied. We will give some non-asymptotic Pierce type estimates. The recursive character of greedy vector quantization allows some improvements to the algorithm of computation of these sequences and the implementation of a recursive formula to quantization-based numerical integration. Furthermore, we establish further properties of sub-optimality of greedy quantization sequences.