This paper presents the Fixed Priority until Zero Laxity (FPZL) scheduling algorithm for multiprocessor realtime systems. FPZL is similar to global fixed priority preemptive scheduling, however, whenever a task reaches a state of zero laxity it is given the highest priority. FPZL is a minimally dynamic algorithm, in that the priority of a job can change at most once during its execution, bounding the number of pre-emptions. Polynomial time and pseudopolynomial time sufficient schedulability tests are derived for FPZL. These tests are then improved by computing upper bounds on the amount of execution that each task can perform in the zero laxity state. An empirical evaluation shows that FPZL is highly effective, with a significantly larger number of task sets deemed schedulable by the tests derived in this paper, than by state-of-the-art schedulability tests for Earliest Deadline until Zero Laxity (EDZL) scheduling.