The left-turn procedures in the Highway Capacity Manual are complex, and some of the equations are presented with little explanation of how they were obtained and the assumptions they embody. This paper is an analytic exploration of two of the four equations used to estimate gq, the amount of green time needed to discharge the opposing queue, and gf, the amount of green time available for through vehicles before the first left-turning vehicle enters the intersection. The investigation reveals surprising hidden assumptions underlying Equation 9-17 for gq, which lead to errors when the opposing flow includes left turns. In the case of Equation 9-20 for gf, the theoretical results are consistently about 5 s larger but otherwise in reasonable agreement with the empirical equation and provide insight into how it could be improved. An analytic approximation is offered either as a replacement or as a framework for an improved empirical model.