  We give a lower and an upper bound for the conformal dimension of the
boundaries of certain small cancellation groups. We apply these bounds to the
few relator and density models for random groups. This gives generic bounds of
the following form, where $l$ is the relator length, going to infinity.
  (a) $1 + 1/C < \Cdim(\bdry G) < C l / \log(l)$, for the few relator model,
and
  (b) $1 + l / (C\log(l)) < \Cdim(\bdry G) < C l$, for the density model, at
densities $d < 1/16$.
  In particular, for the density model at densities $d < 1/16$, as the relator
length $l$ goes to infinity, the random groups will pass through infinitely
many different quasi-isometry classes.
