Cleaves proteins, imported into the mitochondrion, to their mature size. While most mitochondrial precursor proteins are processed to the mature form in one step by mitochondrial processing peptidase (MPP), the sequential cleavage by MIP of an octapeptide after initial processing by MPP is a required step for a subgroup of nuclear-encoded precursor proteins destined for the matrix or the inner membrane. Cleaves precursor proteins of respiratory components, including subunits of the electron transport chain and tricarboxylic acid cycle enzymes, and components of the mitochondrial genetic machinery, including ribosomal proteins, translation factors, and proteins required for mitochondrial DNA metabolism. Release of an N-terminal octapeptide as second stage of processing of some proteins imported into the mitochondrion. Binds 1 zinc ion. Stimulated by Fe(2+). Present with 2690 molecules/cell in log phase SD medium. Belongs to the peptidase M3 family.