Hi Patrick,
How tiny is tiny?  Both the species you mention are usually about a half inch
when fully mature, A. lafresnayi sometimes a bit larger.  If yours are really
tiny, they may be juveniles, which could make them harder to ID.  If they are
really tiny AND have a well developed, mature lip, then they are probably
something else, rather than one of these species.  But as far as mature
specimens of these two Anachis species are concerned, A. avara usually has
about a dozen axial ribs around the body whorl.  A. lafresnayi has a greater
number, usually about twenty.  In A. avara, the ribs on the spire whorls are
restricted to the posterior half to two thirds of the whorl, while in A.
lafresnayi at least some of the ribs cross the entire whorl, suture to
suture.  And, A. avara, when mature, has a couple of denticles or small teeth
on the inner side of the lip, which are not present in A. lafresnayi.  A.
lafresnayi appears in older books as A. translirata.
Regards,
Paul M.