Many critical applications exhibit a growing dependency on Global Navigation Satellite Systems (GNSS), which has led to GNSS jamming and spoofing becoming an increasing threat to society. The Structural Power Content Analysis (SPCA) algorithm is a pre-despreading, low-complexity, and effective method to detect spoofing events, but in practice it is seen that false alarms are being generated in certain jamming scenarios. To mitigate these effects, alternative filtering techniques are evaluated and tested on both simulated data and publicly available spoofing datasets. Effective false alarm reduction with only a minor degradation in spoofing detection sensitivity is demonstrated.