From a real-time perspective, the garbage collector (GC) introduces unpredictable pauses that are not tolerated by real-time tasks. Real-time collectors eliminate this problem but introduce a high overhead. Another approach is to use memory regions (MRs) within which allocation and deallocation is customized. This facility is supported by the memory model of the Real-Time Specification for Java (RTSJ). RTSJ imposes strict access and assignment rules to avoid both the dangling inter-region references and the delays of critical tasks of the GC. A dynamic check solution can incur high overhead, which can be reduced by taking advantage of hardware features. This paper provides an in-depth analytical investigation of the overhead introduced by dynamic assignments checks in RTSJ, describing and analysing several solutions to reduce the introduced overhead.