The development of small-scale self-focusing in a nonlinear Kerr medium after preliminary self-filtering of a laser beam propagating in free space is studied numerically. It is shown that, under definite conditions, due to self-filtering, filamentation instability (beam splitting into filaments) either occurs at significantly larger values of the B-integral, or does not occur at all. In the latter case, there develops the honeycomb instability revealed in this work. This instability is the formation of a random honeycomb structure in the beam cross-section. It is shown that self-filtering can significantly increase the permissible values of the B-integral, at which the beam quality remains acceptable.