  We extend a result regarding the Random Backward Iteration algorithm for
drawing Julia sets (known to work for certain rational semigroups containing a
non-M\"obius element) to a class of M\"obius semigroups which includes certain
settings not yet been dealt with in the literature, namely, when the Julia set
is not a thick attractor in the sense given in [David Fried, Sebastian. M.
Marotta, and Rich Stankewitz, Complex dynamics of M\"obius semigroups, Ergodic
Theory Dynam. Systems, 32(6):1889--1929, 2012].
