The basic single item, continuous review, reorder point inventory control model with given order quantities and a fixed lead time is considered. The objective is to minimize inventory holding cost for the safety stock by determining the reorder point subject to a fill-rate constraint. Several approximations have been suggested for this model. Many of them assume that demand during the lead time follows a normal distribution. In this paper, model approximations assuming normal distributions are contrasted with gamma distributed lead-time demand. It is confirmed numerically, that the simplest approximation is quite accurate under some fairly restrictive conditions. However, it is found that considerable errors can be expected when demand uncertainty is increased, especially when the gamma distribution is applied. Fortunately, the more precise model specification with only marginally increased complexity works quite well, also for the gamma distribution.