The constraints to high levels of milk production imposed by a high-quality-pasture diet, and development of feeding strategies to overcome these limitations, were examined by modelling the nutritional status of New Zealand Friesian and North American Holstein–Friesian dairy cows grazing high-quality pasture. The Cornell Net Carbohydrate and Protein System (CNCPS) was used to predict sensitivity of milk production to a 10 % change in the composition of pasture nutrients. The rate at which fibre and protein were degraded in the rumen and the value given to effective fibre and lignin content significantly affected the supply of metabolisable energy and protein, and the profile of amino acid supply. The first limiting factor in milk production when only high-quality pasture was fed was metabolisable energy supply, while specific amino acids, particularly methionine and lysine, limited milk production when > 20 g/kg diet consisted of a grain supplement. Compared with cows fed a total mixed ration in confinement, North American Holstein–Friesians grazing all pasture produced less milk (29.6 v. 44.1 kg/d). Of the difference in milk production 61 % could be attributed to a lower DM intake (19 kg/d v. 23.4 kg/d). Predictions using the CNCPS indicated that supply of metabolisable energy was the first-limiting factor for milk production from high-quality pasture (251 g crude protein (N× 6.25)/kg, 432 g neutraldetergent fibre/kg, 77 % in vitro DM digestibility), rather than metabolisable protein or amino acids. In addition, these nutritional limitations imposed by pasture diets will be greater for dairy cow genotypes that have not been selected for high performance within a pasture system.