It is shown in this paper that the problem of deciding if a test suite generated from a finite state machine provides complete fault coverage can be converted into the problem of minimizing the test tree representing the test suite. A fault coverage analysis procedure, capable of deciding if a given test suite provides complete fault coverage in respect to a given FSM specification, is then developed. The core of this procedure is a state minimization procedure developed specifically for the class of FSMs whose graphic representations are trees. The fault coverage analysis procedure can cope with partially specified FSM specifications which need not be reduced and faults that increase the number of states up to a chosen upper bound. Two necessary and one sufficient conditions, which in some cases may simplify the fault coverage analysis, are also presented.< >