  We extend some rate of convergence results of greedy quantization sequences
already investigated in arXiv:1409.0732 [math.PR]. We show, for a more general
class of distributions satisfying a certain control, that the quantization
error of these sequences have an $n^{-\frac1d}$ rate of convergence and that
the distortion mismatch 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.
