With the proliferation of smart voice-controlled systems, the vulnerability exhibited by voice-based IOT applications necessitates diligent attention. Voice anti-spoofing provides effective countermeasures by detecting spoofed speech utterances using machine learning (ML). Compared to conventional ML, deep neural networks (DNNs) show significantly higher effectiveness for anti-spoofing, albeit usually requiring extremely powerful computational resources not suitable for deployment on resource-constrained systems. Thus, new techniques are needed to accelerate and compress models while maintaining inference effectiveness. In this work, we investigate existing general-purpose compression methods and novel task-specific compression methods for voice anti-spoofing. We evaluate models on efficiency and effectiveness across various platforms including low-resource devices and high-performance computing machines. In our evaluation, the best general-purpose compression shows an 80.55% inference efficiency improvement with an increase in EER of about 10%, while the best method of task-specific compression yields a 96.63% inference efficiency improvement with an EER increase of 5.4%. Our code is open-source at github.com/yuangongnd/efficient-voice-antispoof.