  We show that the number of half-supersymmetric p-branes in the Type II
theories compactified on orbifolds is determined by the wrapping rules recently
introduced, provided that one accounts correctly for both geometric and
non-geometric T-dual configurations. Starting from the Type II theories
compactified on K3, we analyze their toroidal dimensional reductions, showing
how the resulting half-supersymmetric p-branes satisfy the wrapping rules only
by taking into account all the possible higher-dimensional origins. We then
consider Type II theories compactified on the orbifold T^6/(Z_2 \times Z_2 ),
whose massless four-dimensional theory is an N=2 supergravity. Again, the
wrapping rules are obeyed only if one includes the complete orbit of the
T-duality group, namely either Type IIA or Type IIB theories compactified on
either the geometric or the non-geometric T-dual orbifold. Finally, we comment
on the interpretation of our results in the framework of the duality between
the Heterotic string compactified on K3 \times T^2 and the Type II string
compactified on a Calabi-Yau threefold.
