Milk composition in fatty acids (FA) portrays a class of novel traits of interest for both human health and animal robustness. With the exception of Wallonia, Luxembourg is currently the only place in the world where, using mid-infrared spectrometry, milk composition in 29 FA is routinely recorded for dairy cows. Since 2007, spectral data has been recorded so far on 87,368 cows from 690 different herds, by 2 main control methods (T-method: one sample of only one milking, morning or evening, and S-method: proportionate sample of all daily milkings). Additionally, milk, fat and protein yields are available since 1990. The availability of FA allows many options for management use and animal breeding but requires advanced modeling (e.g., adapted to the testing methods). In the context of animal breeding, genomic selection has been widely developed in dairy cattle, where single-step approach (ssGBLUP) is particularly well suited for small-sized populations, as the dairy cattle population of Luxembourg (365,892 animals currently in pedigree) and is completely integrated into mixed modeling of phenotypic data. The objectives of this study were: (1) to assess the potential benefits of a single-step genomic evaluation on milk FA composition in a small-sized population and in particular (2) to quantify the impact of genomic information on reliability (REL) of estimated breeding values (EBV) of FA in Luxembourg. In a preliminary study for a single FA, oleic acid (C18:1 cis 9) genetic evaluations were performed on 47,613 milk records; collected by S-method, from 8,000 cows in first parity with a random regression test-day model using second order Legendre polynomials. For this sample, molecular data was simulated for 422 AI sires, ancestors of recorded cows. Prediction error variances (PEV) were used to compute REL and effective daughter contributions (EDC). First results showed a low increase in REL and EDC. Extension of this research to all sampling methods and research on the optimum structure of the reference population ...