Two classes of incompletely specified sequential machine (ISSM) are described, which contain the class of input-restricted machines defined by McCluskey [1] and Unger [2] as special cases. These new classes of machine can be identified at the conclusion of a modified (and more efficient) version of the standard compatible pairs-table analysis of Paull and Unger [3]. For such machines only maximal compatible classes need be considered in finding the minimal state machine, and any such covering selection is also closed. An algorithm is presented which is fast and efficient both for hand-use and computer implementation.