Estimating the position of someone's head is a difficult problem with many potential uses. Many methods almost solved head pose estimation problems but They are not suitable for edge devices and embedded systems because they are computationally expensive. In this paper, a deep learning network based on a modified MobileNetV3 architecture is proposed to reduce the computational cost with results comparable to heavy methods. The proposed method is pruned to achieve even less computational cost and results in a network that is ideal for edge devices and smartphones. The architecture used is MobileNetV3Small which has more inverted residual blocks, making it able to inherit MobileNetV3Large performance but with less width, followed by dense layers. Pruning is enhanced by estimating layer importance and resource reallocation, for the informative layers to be less affected by pruning and also to improve performance. In the experiments, the proposed model performs better than many existing heavies with 3.46 MAE before the pruning and 3.61 MAE after the pruning, even though the model has six times fewer parameters than the others and its inference time is about 7ms.