A wealth of information has accumulated about the physiology, genetics and molecular biology of the cell cycle in the fission yeast, Schizosaccharomyces pombe. From this information we have constructed a detailed molecular mechanism of M-phase control based on the modification of M-phase promoting factor (MPF) by a suite of protein kinases (e.g. Wee1 and Mik1 which inhibit MPF) and phosphatases (e.g. Cdc25 which activates MPF). In particular, we analyze the interphase checkpoint in S. pombe, where the wild-type cell confirms that S phase is complete and that the cell is large enough to finish the division cycle. In our model, incomplete DNA replication restrains the onset of M phase by inhibiting Cdc25 and activating Mik1, whereas increasing size biases the cell towards mitosis by down-regulating Wee1. By standard mathematical methods of chemical kinetics, we show that our model gives a quantitatively accurate account of the effects of hydroxyurea treatments, nutritional shifts and other perturbations of the division cycle of wild-type and mutant cells.