Recent experiments support 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 develop a theory based on stochastic hybrid systems which could explain the main division strategies, including not only the adder strategy but the whole range from sizer to timer. We use experiments to explore the division control of E. coli growing with glycerol as carbon source. In this medium, the division strategy is sizerlike, which means that the added size decreases with the size at birth. We found, as our theory predicts, that in a sizerlike 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.