This paper reaffirms that fixed-priority with preemption threshold (FPPT) is an important form of real-time scheduling algorithm, which fills the gap between fixed-priority preemptive (FPP) and fixed-priority non-preemptive (FPNP). However, the known schedulability test is incorrect. A correct schedulability test is presented by extending the idea of the level-i busy period. As well, when a task set is schedulable by FPPT, there may exist multiple valid preemption threshold assignments, which provide useful scheduling options. All valid assignments form a solution space that is delimited by a minimal and maximal assignment. A mechanism is presented to generate part of the valid assignments once the minimal and maximal assignments are known. The known algorithm to compute the minimal assignment starts at FPP, and the known algorithm to compute the maximal assignment starts from any valid assignment. This paper presents algorithms to compute the minimal and maximal assignments starting from FPNP, and the proofs for the correctness of these algorithms are also presented.