OH alkane reactions play a central role in atmospheric and combustion chemistry, and accurate modeling requires accurate knowledge of their rate constants over a wide temperature range. We present data for 10 OH radical - alkane reactions over the temperature range 300-400 K and then combine our data with other literature data to find optimally estimated Arrhenius parameters using a modified Arrhenius form consistent with transition state theory. This modified form explicitly accounts for the loose modes in the transition state that cause curvature in Arrhenius plots. It thus fits data over a wide temperature range in a realistic manner, allowing precise comparison of data sets covering different temperature ranges. By comparing our data with other published data, we establish that most of these rate constants are now known to better than 5% accuracy over the 300-400 K temperature range.