  If neutrino masses are obtained via the canonical seesaw mechanism, based on
an underlying 2X2 mass matrix, unitarity violation of the neutrino mixing
matrix is unavoidable, but its effect is extremely small. On the other hand, in
the inverse (and linear) seesaw mechanisms, based on an underlying 3X3 mass
matrix, it can be significant and possibly observable. This 3X3 matrix is
examined in more detail, and a NEW variation (the lopsided seesaw) is proposed
which has features of both mechanisms. A concrete example based on U(1)_N is
discussed.
