  Semiconstrained systems were recently suggested as a generalization of
constrained systems, commonly used in communication and data-storage
applications that require certain offending subsequences be avoided. In an
attempt to apply techniques from constrained systems, we study sequences of
constrained systems that are contained in, or contain, a given semiconstrained
system, while approaching its capacity. In the case of contained systems we
describe to such sequences resulting in constant-to-constant bit-rate block
encoders and sliding-block encoders. Surprisingly, in the case of containing
systems we show that a "generic" semiconstrained system is never contained in a
proper fully-constrained system.
