Recent experiments have supported the Adder model for E. coli division control. This model posits that bacteria grow, on average, a fixed size before division. It also predicts decorrelation between the noise in the added size and the size at birth. Here we use new experiments and a theoretical approach based on continuous rate models to explore deviations from the adder strategy, specifically, the division control of E. coli growing with glycerol as carbon source. In this medium, the division strategy is sizer-like, which means that the added size decreases with the size at birth. We found that in a sizer-like strategy the mean added size decreases with the size at birth while the noise in added size increases. We discuss possible molecular mechanisms underlying this strategy, and propose a general model that encompasses the different division strategies.