We use data from 50 earthquakes in southern California to test the accuracy of event parameter determination using single seismic stations for the purpose of early warning. Earthquake magnitude, hypocentral distance, and backazimuth are all estimated using P-wave arrivals only. There is a wide range in the accuracy of event parameters determined by different seismic stations. One quarter of the stations produced magnitude estimates with errors less than ±0.3 magnitude units, hypocentral distances within ±15 km, and backazimuth calculations within ±20°. This accuracy is sufficient to provide useful early warning. Using P-wave arrivals is the most rapid method of delivering earthquake early warning and may permit a few seconds notice of impending ground motion even in the epicentral region. Our results show that networks using a P-wave detection approach for early warning can increase the accuracy of magnitude estimations by determining station-specific scaling relations between the predominant period of the P wave and event magnitude and by utilizing stations with optimal relations. Further, because individual stations are able to deliver an accurate early warning, the option of utilizing the technology in regions that lack a dense seismic network but are in need of seismic hazard mitigation becomes possible.