Truth maintenance systems have been used in several recent problem solving systems to record justifications for deduced assertions, to track down the assumptions which underlie contradictions when they arise, and to incrementally modify assertional data structures when assumptions are retracted. A TMS algorithm is described here that is substantially different from previous systems. This algorithm performs deduction in traditional propositional logic in such a way that the premise set from which deduction is being done can be easily manipulated. A novel approach is also taken to the role of a TMS in larger deductive systems. In this approach the TMS performs all propositional deduction in a uniform manner while the larger system is responsible for controlling the instantiation of universally quantified formulae and axiom schemas.