In New Zealand, a specific selection scheme for the dairy cattle population milked once-a-day (OAD) has not been implemented. This study aims to investigate estimated genetic progress for different selection objectives based on selection scheme designs using progeny testing (PT) and genomic selection (GS) in OAD herds. Under a PT-scheme, estimated genetic progress ranged from 7 to 45 kg/year (milk), 2.18–2.24 kg/year (fat), and 0.83–1.71 kg/year (protein). Conversely, genetic gains resulting from selecting bulls generated in twice-a-day (TAD) milking systems and used to inseminate cows in OAD herds, ranged between 12 and 52 kg/year (milk), 2.34 and 3.22 kg/year (fat) and 0.83 and 2.29 kg/year (protein). Correlated responses tend to be greater in the yield traits when the emphasis on fertility, residual survival and body condition score were reduced in the selection objective. Further correlated responses in yield traits were reduced when type-related traits were included in the selection objective, in particular when bulls were tested in TAD systems. A more immediate and profitable alternative might be the implementation of a GS-scheme, that would result in a faster genetic gain in the aggregate breeding value or merit for all the traits included in the selection objective (0.310–0.368 vs 0.191–0.196 σg/yr).