Efficient diet design requires accurate predictions of the relationship between nutrient inputs and milk output. The NRC (2001) model has been shown to be biased in predicting overall milk production and production responses to varying dietary protein intake and exhibits relatively low precision (~25% RMSE). The objective of this work was to test revised representations of the relationship between nutrient supply and milk protein production. Data used were from 237 published studies containing 724 treatment means. Microbial protein outflows were predicted from Roman-Garcia et al. (2016), and RUP flows from White et al. (2017). The AA composition of protein flows was from Sok et al. (2017). Digestibility of the RUP AA was from Paz-Manzano et al. (2014). Two model forms were tested: Milk Protein = DEI + EAA_i + EAA_i² + NEAA + St + FA + Milk Fat % + DIM (1); and Milk Protein = DEI + EAA_i + (EAA_i/DEI)² + NEAA + St + FA + Milk Fat % + DIM (2) where DEI represented digestible energy intake, EAA the digested supply (g/d) of the ith essential AA, NEAA the digested total supply of other AA, and St and FA dietary starch and fatty acid contents (% of DM). Essential AA included all except Trp. All combinations of EAA terms were tested with the presence of squared terms requiring linear term presence. The best submodel for eqn. (1) contained terms for DEI, Arg, Leu, Lys, Met, Thr, NEAA, St, DIM, and milk fat with an AICc of 8191 and RMSE of 12.5%. The best submodel for eqn. (2) contained the same terms plus Phe with an AICc of 8173 and RMSE of 11.9%. Exclusion of His, Ile, and Val from both models indicates they are always provided in excess, or there is inadequate independent variance to define responses to those AA. The results indicate that expressing declining efficiency of AA use for milk protein production as a square of the ratio of AA to DEI is superior to the square of AA. These equations demonstrate that responses to individual EAA and energy are additive and our models must reflect that if improved accuracy and precision are to be achieved in diet formulation.