The aim of this study was to investigate the effect of milk flow rate and milk allowance on calves’ use of a computer controlled milk feeder. Six blocks, each consisting of 16 calves, were used (Holstein–Friesian, Danish Red, and Jersey). Within each block, the calves were assigned to one of four treatments: low milk allowance and normal milk flow rate (LN), high milk allowance and normal milk flow rate (HN), low milk allowance and reduced milk flow rate (LR), or high milk allowance and reduced milk flow rate (HR). A low milk allowance consisted of 4.8 l of milk daily for the heavy breeds (Holstein–Friesian, Danish Red) and 2.8 l for Jersey, while high milk allowance were 8.0 l daily for the heavy breeds and 4.8 l for Jersey. The data collected automatically by the computer controlled milk feeder from day 15 until weaning showed that overall the combination of high milk allowance and reduced milk flow rate resulted in most time spent in the feeder during rewarded visits ( P<0.01). However, there were significant breed effects. For calves of the heavy breeds a reduced milk flow rate resulted in a longer duration of rewarded visits ( P<0.01) and in a longer duration of all visits ( P<0.05). Also for calves of the heavy breeds, a high milk allowance resulted in fewer unrewarded visits ( P<0.05), a shorter duration of unrewarded visits ( P<0.01), and a shorter duration of all visits to the feeder ( P<0.05). Furthermore, across breeds the reduced milk flow rate resulted in a longer duration of visits where the calves had access to milk but did not consume any ( P<0.05). The behaviour of the calves was recorded for 24 h using video. These recordings showed that for the heavy breeds, the calves fed at a reduced milk flow rate occupied the feeder more than calves fed at a normal milk flow rate ( P<0.05). The calves of the heavy breeds offered a high milk allowance entered a free feeder less often ( P<0.05) and also entered the feeder less frequently as soon as it was free ( P<0.05). Across breeds, the calves offered a low milk allowance in combination with a reduced milk flow rate tried more often to get access to an occupied feeder ( P<0.05) and displaced other calves from the feeder more often ( P<0.05). No effect of treatment was found on the occurrence of cross-sucking. The results show that for the heavy breeds, a reduced milk flow rate increased the mean occupancy of the feeder due to a longer duration of rewarded visits. Furthermore, for the heavy breeds a higher milk allowance reduced the mean occupancy through a reduction in the duration of unrewarded visits. These results support the hypothesis that a high number of unrewarded visits to computer controlled milk feeders may be due to hunger. They further suggest that the time the calves occupy the feeder may be reduced by a high milk allowance. The combination of a low milk allowance and a reduced milk flow rate may result in an increase in the competition for access to the feeder.