Visual grounding is an essential capability of Visual Language Models (VLMs) to understand the real physical world. Previous state-of-the-art grounding visual language models usually have large model sizes, making them heavy for deployment and slow for inference. However, we notice that the sizes of visual encoders are nearly the same for small and large VLMs and the major difference is the sizes of the language models. Small VLMs fall behind larger VLMs in grounding because of the difference in language understanding capability rather than visual information handling. To mitigate the gap, we introduce 'Efficient visual Grounding language Models' (EGM): a method to scale the test-time computation (#generated tokens). Scaling the test-time computation of a small model is deployment-friendly, and yields better end-to-end latency as the cost of each token is much cheaper compared to directly running a large model. On the RefCOCO benchmark, our EGM-Qwen3-VL-8B demonstrates 91.4 IoU with an average of 737ms (5.9x faster) latency while Qwen3-VL-235B demands 4,320ms to achieve 90.5 IoU. To validate our approach's generality, we further set up a new amodal grounding setting that requires the model to predict both the visible and occluded parts of the objects. Experiments show our method can consistently and significantly improve the vanilla grounding and amodal grounding capabilities of small models to be on par with or outperform the larger models, thereby improving the efficiency for visual grounding.