  We prove logarithmic conditional stability up to the final time for
backward-parabolic operators whose coefficients are Log-Lipschitz continuous in
$t$ and Lipschitz continuous in $x$. The result complements previous
achievements of Del Santo and Prizzi (2009) and Del Santo, Jaeh and Prizzi
(2015), concerning conditional stability (of a type intermediate between
Hoelder and logarithmic), arbitrarily closed, but not up to the final time.
