  We study a system of fermions in one spatial dimension with linearly
confining interactions and short-range disorder. We focus on the zero
temperature properties of this system, which we characterize using bosonization
and the Gaussian variational method. We compute the static compressibility and
ac conductivity, and thereby demonstrate that the system is incompressible, but
exhibits gapless optical conductivity. This corresponds to a "Mott-glass"
state, distinct from an Anderson and a fully gapped Mott insulator, arising due
to the interplay of disorder and charge confinement. We argue that this
"Mott-glass" phenomenology should persist to non-zero temperatures.
