  We demonstrate that the tail of transmission distribution through 1D
disordered Anderson chain is a strong function of the correlation radius of the
random potential, $a$, even when this radius is much shorter than the de
Broglie wavelength, $k_F^{-1}$. The reason is that the correlation radius
defines the phase volume of the trapping configurations of the random
potential, which are responsible for the low-$T$ tail. To see this, we perform
the averaging over the low-$T$ disorder configurations by first introducing a
finite lattice spacing $\sim a$, and then demonstrating that the prefactor in
the corresponding functional integral is exponentially small and depends on $a$
even as $a \to 0$. Moreover, we demonstrate that this restriction of the phase
volume leads to the dramatic change in the shape of the tail of ${\cal P}(\ln
T)$ from universal Gaussian in $\ln T $ to a simple exponential (in $\ln T $)
with exponent depending on $a$. Severity of the phase-volume restriction
affects the shape of the low-$T$ disorder configurations transforming them from
almost periodic (Bragg mirrors) to periodically-sign-alternating (loose
mirrors).
