  A new quasi-particle basis of states is presented for all the irreducible
modules of the M(3,p) models. It is formulated in terms of a combination of
Virasoro modes and the modes of the field phi_{2,1}. This leads to a fermionic
expression for particular combinations of irreducible M(3,p) characters, which
turns out to be identical with the previously known formula. Quite remarkably,
this new quasi-particle basis embodies a sort of embedding, at the level of
bases, of the minimal models M(2,2k+1) into the M(3,4k+2-delta) ones, with 0
\leq delta \leq 3.
