  We consider unitary analogs of $d-$dimensional Anderson models on $l^2(\Z^d)$
defined by the product $U_\omega=D_\omega S$ where $S$ is a deterministic
unitary and $D_\omega$ is a diagonal matrix of i.i.d. random phases. The
operator $S$ is an absolutely continuous band matrix which depends on
parameters controlling the size of its off-diagonal elements. We adapt the
method of Aizenman-Molchanov to get exponential estimates on fractional moments
of the matrix elements of $U_\omega(U_\omega -z)^{-1}$, provided the
distribution of phases is absolutely continuous and the parameters correspond
to small off-diagonal elements of $S$. Such estimates imply almost sure
localization for $U_\omega$.
