Is a relatively unspecific dipeptidase cleaving a variety of dipeptides, notably those with an N-terminal beta-Ala or D-Ala residue, e.g. carnosine (beta-Ala-His). To a lesser extent, also shows aminopeptidase activity, since it is able to catalyze the removal of the N-terminal amino acid from a few distinct tripeptides. Binds 2 Zn(2+) ions per subunit. These two catalytic ions are both involved in the stabilization of the tetrahedral intermediate and in the activation of the catalytic water molecule. Fully inhibited by 1,10-phenanthroline or EDTA. Belongs to the peptidase M20A family.