Maximum Satisfiability (MaxSAT) and its weighted and partial variants are well-known optimization formulations of Boolean Satisfiability (SAT). MaxSAT consists of finding an assignment that satisfies the (possibly empty) set of hard clauses, while minimizing the sum of weights of the falsified soft clauses. Recent years have witnessed the development of complete algorithms for MaxSAT motivated by a number of practical applications. The most effective approaches in such practical settings are based on iteratively calling a SAT solver and computing unsatisfiable cores to guide the search. Such approaches use computed unsatisfiable cores from unsatisfiable (UNSAT) outcomes to relax the soft clauses occurring in the computed cores. Surprisingly, only recently has an approach been proposed that exploits models from satisfiable (SAT) outcomes [1], [2] rather than unsatisfiable cores from UNSAT outcomes. This paper proposes two novel MaxSAT algorithms which exploit SAT outcomes to relax soft clauses taking into account the computed models. The new algorithms are shown to outperform classical MaxSAT algorithms and to be fairly competitive with recent core-guided MaxSAT algorithms. Finally, a well-known core-guided MaxSAT algorithm is extended to additionally exploit computed models in an attempt to integrate both approaches.