During the past decades of research in Real-Time systems, non-preemptive scheduling and fully preemptive scheduling have been extensively investigated, as well as compared with each other. However, it has been shown that none of the two scheduling paradigms dominates over the other in terms of schedulability. In this context, Limited Preemptive Scheduling (LPS) has emerged as an attractive alternative with respect to, e.g., increasing the overall system schedu- lability, efficiently reducing the blocking by lower priority tasks (compared to non-preemptive scheduling) as well as efficiently controlling the number of preemptions, thus controlling the overall preemption-related delay (compared to fully-preemptive scheduling). Several approaches within LPS enable the above mentioned advantages. In our work, we consider the Fixed Preemption Point Scheduling (LP-FPP) as it has been proved to effectively reduce the preemption-related delay compared to other LPS approaches. In particular, LP-FPP facilitates more precise estimation of the preemption-related delays, since the preemption points of a task in LP-FPP are explicitly selected during the design phase, unlike the other LPS approaches where the preemption points are determined at runtime. The main goal of the proposed work is to improve the schedulability of real-time systems under the LP-FPP approach. We investigate its use in different domains, such as: single core hard real-time systems, partitioned multi-core systems and real-time systems which can occasionally tolerate deadline misses. We enrich the state of the art for the single core hard real-time systems by proposing a novel cache-related preemption delay analysis, towards reducing the pessimism of the previously proposed methods. In the context of partitioned multi-core scheduling we propose a novel partitioning criterion for the Worst-Fit Decreasing based partitioning, and we also contribute with the comparison of existing partitioning strategies for LP-FPP scheduling. Finally, in the context of real-time systems which can occasionally tolerate deadline misses, we contribute with a probabilistic response time analysis for LP-FPP scheduling and a preemption point selection method for reducing the deadline-misses of the tasks.