Summary: We consider several combinatorial principles satisfied for cardinals smaller than \(\operatorname{cov} (\mathcal M)\), the covering number of the ideal of first category sets of the real line. Using these principles we prove that there exist N\(_0\)-sets (similarly N-sets, A-sets) which cannot be covered by fewer than \(\operatorname{cov}(\mathcal M)\) pD-sets (A-sets, N-sets, respectively). This improves the results of our previous paper [ibid. 125, 1111-1121 (1997; Zbl 0871.42007)].