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Background Many organisms coordinate cell growth and division through size control mechanisms: cells must reach a critical size to trigger some cell cycle event. Bacterial division is often assumed to be controlled in this way, but experimental evidence to support this assumption is still lacking. Theoretical arguments show that size control is required to maintain size homeostasis in the case of exponential growth of individual cells. Nevertheless, if the growth law deviates slightly from exponential in very small cells, homeostasis can be maintained with a simple "timer" triggering division. Therefore, deciding whether division control in bacteria relies on a "timer" or "sizer" mechanism requires quantitative comparisons between models and data. Results The "timer" and "sizer" hypotheses find a natural expression in models based on Partial Differential Equations. Here we confront these models with recent data on Escherichia coli single cell growth. We demonstrate that a size-independent "timer" mechanism for division control, though theoretically possible, is quantitatively incompatible with the data and extremely sensitive to slight variations in the growth law. In contrast, a "sizer" model is robust and fits the data well. In addition, we tested the effect of variability in individual growth rates and noise in septum positioning and found that size control is robust to this phenotypic noise. Conclusions Confrontations between cell cycle models and data usually suffer from a lack of high-quality data and suitable statistical estimation techniques. Here we overcome these limitations by using high precision measurements of tens of thousands of single bacterial cells combined with recent statistical inference methods to estimate the division rate within the models. We therefore provide the first precise quantitative assessment of different cell cycle models. [ABSTRACT FROM AUTHOR]