  We study a model for the Nematic--Smectic-A (NA) transition in aerogel, and
find that even arbitrarily weak quenched disorder (i.e., low aerogel density)
destroys translational (smectic) order. Ignoring elastic anharmonicities, but
keeping anharmonic couplings to disorder, leads to the prediction that there is
no ``Bragg glass'' phase in this system: it is riddled with dislocation loops
induced by the quenched disorder. Orientational (nematic) order is destroyed as
well, as is the thermodynamically sharp NA transition, in agreement with recent
experimental results.
