When an implementation under test (IUT) is state-based, and its expected abstract behavior is given in terms of a fi- nite state machine (FSM), a checking sequence generated from the specification FSM and applied on the IUT for test- ing can provide us with high-level confidence in the cor- rect functional behavior of our implementation. One of the issues here is to generate efficient checking sequences in terms of their lengths. In this paper, we discuss the possi- bility of reducing the lengths of checking sequences by mak- ing use of the invertible transitions in the specification FSM to increase the choice of -sequences to be included into a checking sequence. We present a sufficient condition for adopting alternative -sequences and illustrate a possible way of incorporating these alternative -sequences into ex- isting methods for checking sequence generation to further reduce their lengths. Keywords: conformance testing, finite state machine, checking sequence, distinguishing sequence.