We use a dataset of 87,000 independent UK companies to investigate the relationship between firm size and growth. For the sample as a whole, a Galton-Markov model of regression towards the mean shows that growth is negatively related to initial size. However, when the sample is broken down by size group, we find that regression towards the mean only occurs for the smallest firms, e.g. those with eight employees or less. For larger firms, there is essentially no relationship between growth and size. Even for the smallest firm, our results may be due to transitory factors.