This paper presents theoretical analysis of left-turn operations under heavy traffic. When traffic demand is heavy, residual queues from previous cycles may occur and contribute to blockage of the left-turn bay by adjacent through traffic. Such blockage reduces the left-turn capacity and is a random phenomenon. An improved model for protected left-turn capacity is first proposed, taking into account the influence of residual queues and blockage by through traffic. In addition, the classic model always overestimates the potential permitted left-turn capacity when opposing traffic is heavy. The potential permitted left-turn capacity is then modeled in a probabilistic way, and a simple estimation is suggested by investigating its relation to the classic model. Furthermore, because left-turn capacity may vary in response to a blockage, the coefficients of variance for protected left-turn capacity and for queue clearance time are introduced to evaluate the protected left-turn timing plan. The developed analytical models are validated with CORSIM simulations.