Despite its potential utility for predicting cows' milk yield responses to once-daily milking (ODM), the genetic basis of cow milk trait responses to ODM has been scarcely if ever described in the literature, especially for short ODM periods. This study set out to (1) estimate the genetic determinism of milk yield and composition during a 3-wk ODM period, (2) estimate the genetic determinism of milk yield responses (i.e., milk yield loss upon switching cows to ODM and milk yield recovery upon switching them back to twice-daily milking; TDM), and (3) seek predictors of milk yield responses to ODM, in particular using the first day of ODM. Our trial used 430 crossbred Holstein × Normande cows and comprised 3 successive periods: 1 wk of TDM (control), 3 wk of ODM, and 2 wk of TDM. Implementing ODM for 3 wk reduced milk yield by 27.5% on average, and after resuming TDM cows recovered on average 57% of the milk lost. Heritability estimates in the TDM control period and 3-wk ODM period were, respectively, 0.41 and 0.35 for milk yield, 0.66 and 0.61 for milk fat content, 0.60 and 0.80 for milk protein content, 0.66 and 0.36 for milk lactose content, and 0.20 and 0.15 for milk somatic cell score content. Milk yield and composition during 3-wk ODM and TDM periods were genetically close (within-trait genetic correlations between experimental periods all exceeding 0.80) but were genetically closer within the same milking frequency. Heritabilities of milk yield loss observed upon switching cows to ODM (0.39 and 0.34 for milk yield loss in kg/d and %, respectively) were moderate and similar to milk yield heritabilities. Milk yield recovery (kg/d) upon resuming TDM was a trait of high heritability (0.63). Because they are easy to measure, TDM milk yield and composition and milk yield responses on the first day of ODM were investigated as predictors of milk yield responses to a 3-wk ODM to easily detect animals that are well adapted to ODM. Twice-daily milking milk yield and composition were found to be partly genetically correlated with milk yield responses but not closely enough for practical application. With genetic correlations of 0.98 and 0.96 with 3-wk ODM milk yield losses (in kg/d and %, respectively), milk yield losses on the first day of ODM proved to be more accurate in predicting milk yield responses on longer term ODM than TDM milk yield.