  We show that a rank reduction technique for string C-group representations
first used for the symmetric groups generalizes to arbitrary settings. The
technique permits us, among other things, to prove that orthogonal groups
defined on $d$-dimensional modules over fields of even order greater than 2
possess string C-group representations of all ranks $3\leq r\leq d$. The broad
applicability of the rank reduction technique provides fresh impetus to
construct, for suitable families of groups, string C-groups of highest possible
rank. It also suggests that the alternating group ${\rm Alt}(11)$---the only
known group having `rank gaps'---is perhaps more unusual than previously
thought.
