In global real-time multiprocessor scheduling, a recent analysis technique for Task-level Fixed-Priority (TFP) scheduling has been shown to outperform many of the analyses for Job-level Fixed-Priority (JFP) scheduling on average. Since JFP is a generalization of TFP scheduling, and the TFP analysis technique itself has been adapted from an earlier JFP analysis, this result is counter-intuitive and in our opinion highlights the lack of good JFP scheduling techniques. Towards generalizing the superior TFP analysis to JFP scheduling, we propose the Smallest Pseudo-Deadline First (SPDF) JFP scheduling algorithm. SPDF uses a simple task-level parameter called pseudo-deadline to prioritize jobs, and hence can behave as a TFP or JFP scheduler depending on the values of the pseudodeadlines. This natural transition from TFP to JFP scheduling has enabled us to incorporate the superior TFP analysis technique in an SPDF schedulability test. We also present a pseudo-deadline assignment algorithm for SPDF scheduling that extends the well-known Optimal Priority Assignment (OPA) algorithm for TFP scheduling. We show that our algorithm is optimal for the derived schedulability test, and also present a heuristic to overcome the computational complexity issue of the optimal algorithm. Our simulation results show that the SPDF algorithm with the new analysis significantly outperforms state-of-the-art TFP and JFP analysis.