  We study the transition from the cholesteric phase to two TGB$_C$ phases near
the upper critical twist $k_{c2}$: the Renn-Lubensky TGB$_C$ phase, with layer
normal rotating in a plane perpendicular to the pitch axis, and the Bordeaux
TGB$_C$ phase, with the layer normal rotating on a cone parallel to the pitch
axis. We calculate properties, including order-parameter profiles, of both
phases.
