The control of cell proliferation under steady-state conditions in the budding yeast, Saccharomyces cerevisiae, is well described by either the tandem or sloppy size control models, both of which suggest that differences in cycle time between individual cells or between parents and daughters is largely due to differences in birth size. These models have been investigated further under conditions in which cell size has not been a rate-determining factor for cell cycle initiation. Two approaches have been used. The first involves the growth of cells in low concentrations of hydroxyurea (HU), which has the effect of prolonging the duration of DNA synthesis. This leads to a lengthening of the budded period, which in turn leads to daughter cells being larger at division than the normal cell cycle initiation size of daughters in steady-state populations. The second approach involves the accumulation of cells at the key control point of the cycle, called start, using the pheromone alpha-factor. Since growth is unaffected, all cells eventually become larger than the volume at which they would normally initiate the cell cycle. The kinetics of proliferation were followed after release from alpha-factor arrest. The results from both approaches were broadly consistent with the predictions of both models. However, abolition of birth-size differences between parents and daughters in the presence of HU did not lead to a complete disappearance of differences in either cycle time or proliferation kinetics. Furthermore, following release from alpha-factor arrest, the rate of cell cycle initiation of parent cells was slower than in steady-state culture and the daughters' cells behaved as if comprising two separate populations. These discrepancies suggest that besides a size difference, there are additional physiological differences between parent and daughter cells.