The determination of aquifer parameters is fundamental to groundwater resources assessment. This important topic has received much attention in the literature over many years. Singh (2008) presented a method for determination of parameters for an ideal confined aquifer, based on early drawdown data. The Theis well function (Theis 1935), the topic of interest here, arises as a core part of the analysis. It is, of course, essential that approximations to the Theis well function be robust and accurate so that reliable estimates of aquifer parameters are obtained. Two approximations for the Theis well function were presented by Singh (2008). The purposes of this discussion were (1) to examine these two approximations, in particular their relative error as reported by the author, and (2) to alert readers to an existing, easy-to-calculate approximation to the Theis well function.