Fixed priority preemption threshold scheduling (FPTS) may significantly improve the schedulability ratio of task sets compared to both fixed-priority pre-emptive scheduling (FPPS) and fixed-priority non-preemptive scheduling (FPNS). Moreover, FPTS reduces stack memory requirements compared to FPPS. Unfortunately, the scheduling policy defined by the standard automotive platform AUTOSAR/OSEK only supports a restricted version of FPTS. In earlier work, the consequences of these limitations have been investigated for the schedulability ratio of task sets on a uniprocessor platform. This paper considers the consequences for the stack memory requirements. To that end, it presents a preemption threshold assignment algorithm for minimizing stack usage under FPTS on an AUTOSAR/OSEK platform. The paper includes a comparative evaluation of the stack usage of FPTS without restrictions and FPTS as defined by AUTOSAR/OSEK.