  Modal Transition Systems (MTS) are a well-known formalism that extend
Labelled Transition Systems (LTS) with the possibility of specifying necessary
and permitted behaviour. Modal refinement ($\preceq_m$) of MTS represents a
step of the design process, namely the one in which some optional behaviour is
discarded while other optional behaviour becomes necessary. Whenever two MTS
are not in modal refinement relation, it could still be the case that the set
of implementations of one MTS is included in the set of implementations of the
other.
  The challenge of devising an alternative notion of modal refinement that is
both sound and complete with respect to the set of implementations, without
disregarding valuable implementations, remains open. We introduce a subset of
MTS called Non-reducible Modal Transition Systems (NMTS), together with a novel
refinement relation $\preceq_n$ for NMTS. We illustrate through examples the
additional constraints imposed by NMTS. Furthermore, we discuss a property
holding for NMTS whose implementations are non-deterministic.
