Optimization Modulo Theories (OMT) extends Satisfiability Modulo Theories (SMT) with the task of optimizing some objective function(s). In OMT solvers, a CDCL-based SMT solver enumerates theory-satisfiable total truth assignments, and a theory-specific procedure finds an optimum model for each of them; the current optimum is then used to tighten the search space for the next assignments, until no better solution is found. In this paper, we analyze the role of truth-assignment enumeration in OMT. First, we spotlight that the enumeration of total truth assignments is suboptimal, since they may over-restrict the search space for the optimization procedure, whereas using partial truth assignments instead can improve the effectiveness of the optimization. Second, we propose some assignment-reduction techniques for exploiting partial-assignment enumeration within the OMT context. We implemented these techniques in the OptiMathSAT solver, and we conducted an experimental evaluation on \(\text {OMT}\) benchmarks. The results confirm the improvement in both the efficiency of optimal solving and the quality of the obtained solutions for anytime solving.