We determined the τc and τpmax parameters from the K-NET strong motion records of 16 earthquakes in Japan with moment magnitude (Mw) ranging from 6.0 to 8.3. A 0.075 Hz high-pass Butterworth filter was applied for determination of τc based on our previous studies. It was found that different pole selections of the Butterworth filter lead to different uncertainty in magnitude determination. Our results show that using two poles in the filters results in the best magnitude estimates, i.e., minimized the standard deviation in magnitude determination in comparison to Mw using τc. The τpmax parameters (Allen and Kanamori, 2003) were also determined with the same dataset using the Wurman et al. (2007) procedure. It was found that τpmax values obtained from this dataset, and using the Wurman procedure, had a larger uncertainty. However, when a 0.075 Hz high-pass Butterworth filter with five poles was added, the uncertainty in τpmax-derived magnitude estimates decreased minimizing the standard deviation in magnitude determination using τpmax. This difference in the behavior of τc and τpmax can be used to further reduce the uncertainty in rapid magnitude determination for earthquake early warning. When the magnitude estimations from τc and τpmax of each event are averaged to provide a new magnitude estimate, the standard deviation in magnitude estimates is reduced further to 0.27 magnitude units.