The Poincaré-Dulac normalization procedure is based on a sequence of coordinate transformations generated by solutions to homologlcal equations; in the presence of resonances, such solutions are not unique and one has to make some-what arbitrary choices for elements in the kernel of relevant homological operators, different choices producing different higher order effects. The simplest, and usual, choice is to set these kernel elements to zero; here we discuss how a different prescription can lead to a further simplification of the resulting normal form, in a completely algorithmic way.