Circular Trellis Coded Modulation (CTCM) defines a family of (block) trellis codes which use a unique algebraic constraint, imposed on the start state, to produce a strong tail-biting property without the inefficiency of driving the encoder state to zero by using a sequence of input zeroes. From the beginning of CTCM, elements of the Galois field, GF(pm), have served dual roles, labeling both s ystem trellis nodes and valid input symbols. This dual use of field elements facilitates exploitation of the algebraic structure of GF(pm). The system trellis always take a particularly simple and advantageous form (called the pn-fly form) whenever the alphabet of valid input symbols is chosen to be (a coset of) any additive subgroup of the additive group structure of GF(pm). This paperproposes a family of signal mappings that complete the definition of the CTCM system by providing structurally consistent output labels for the trellis edges. The completion of a structural definition greatly facilitates system analysis, especially the (future) geometrically precise construction of a related signal constellation. At the same time, it preserves the possibility of an advantegeous receiver structure.