Face detectors are becoming a crucial component of many applications, including surveillance, that often have to run on edge devices with limited processing power and memory. Therefore, there's a pressing demand for compact face detection models that can function efficiently across resource-constrained devices. Over recent years, network pruning techniques have attracted a lot of attention from researchers. These methods haven't been well examined in the context of face detectors, despite their expanding popularity. In this paper, we implement filter pruning on two already small and compact face detectors, named EXTD (Extremely Tiny Face Detector) and EResFD (Efficient ResNet Face Detector). The main pruning algorithm that we utilize is Filter Pruning via Geometric Median (FPGM), combined with the Soft Filter Pruning (SFP) iterative procedure. We also apply L1 Norm pruning, as a baseline to compare with the proposed approach. The experimental evaluation on the WIDER FACE dataset indicates that the proposed approach has the potential to further reduce the model size of already lightweight face detectors, with limited accuracy loss, or even with small accuracy gain for low pruning rates.