This paper presents and proves totally correct a new algorithm, called QSMA, for the satisfiability of a quantified formula modulo a complete theory and an initial assignment. The optimized variant of QSMA implemented in YicesQS is described and shown to preserve total correctness. A report on the performance of YicesQS at the 2022 SMT competition is included. YicesQS ran in the LIA, NIA, LRA, NRA, and BV categories and ranked second for the “largest contribution” award (single queries). It was the only solver to solve all LRA instances, where it was about 2 orders of magnitude faster than the second best solver (Z3).