  The capability of string theories to reproduce at low energy the observed
pattern of quark and lepton masses and mixing angles is examined, focusing the
attention on orbifold constructions, where the magnitude of Yukawa couplings
depends on the values of the deformation parameters which describe the size and
shape of the compactified space. A systematic exploration shows that for $Z_3$,
$Z_4$, $Z_6$--I and possibly $Z_7$ orbifolds a correct fit of the physical
fermion masses is feasible. In this way the experimental masses, which are
low--energy quantities, select a particular size and shape of the compactified
space, which turns out to be very reasonable (in particular the modulus $T$
defining the former is $T=O(1)$). The rest of the $Z_N$ orbifolds are rather
hopeless and should be discarded on the assumption of a minimal $SU(3)\times
SU(2)\times U(1)_Y$ scenario. On the other hand, due to stringy selection
rules, there is no possibility of fitting the Kobayashi--Maskawa parameters at
the renormalizable level, although it is remarked that this job might well be
done by non--renormalizable couplings.
