This paper investigates the factors influencing the allocation of time between public and private sectors by medical specialists. A discrete choice structural labour supply model is estimated, where specialists choose from a set of job packages that are characterised by the number of working hours in the public and private sectors. The results show that medical specialists respond to changes in earnings by reallocating working hours to the sector with relatively higher earnings, while leaving total working hours unchanged. The magnitudes of the own-sector and cross-sector earnings elasticities fall in the range of 0.21-0.54, and are larger for male than for female specialists. The labour supply response varies by doctors' age and medical specialty. Family circumstances such as the presence of young dependent children influence the hours worked by female specialists but not male specialists. We illustrate the relevance of our findings by simulating the impact of recent trends in earnings growth in the public and private sectors.