Current breeding tools aiming to improve feed efficiency use definitions based on total dry matter intake (DMI); for example, residual feed intake or feed saved. This research aimed to define alternative traits using existing data that differentiate between feed intake capacity and roughage or concentrate intake, and to investigate the phenotypic and genetic relationships among these traits. The data set contained 39,017 weekly milk yield, live weight, and DMI records of 3,164 cows. The 4 defined traits were as follows: (1) Feed intake capacity (FIC), defined as the difference between how much a cow ate and how much she was expected to eat based on diet satiety value and status of the cow (parity and lactation stage); (2) feed saved (FS), defined as the difference between the measured and the predicted DMI, based on the regression of DMI on milk components within experiment; (3) residual roughage intake (RRI), defined as the difference between the measured and the predicted roughage intake, based on the regression of roughage intake on milk components and concentrate intake within experiment; and (4) residual concentrate intake (RCI), defined as the difference between the measured and the predicted concentrate intake, based on the regression of concentrate intake on milk components and roughage intake within experiment. The phenotypic correlations were −0.72 between FIC and FS, −0.84 between FS and RRI, and −0.53 between FS and RCI. Heritability of FIC, FS, RRI, and RCI were estimated to be 0.21, 0.12, 0.15, and 0.03, respectively. The genetic correlations were −0.81 between FS and FIC, −0.96 between FS and RRI, and −0.25 between FS and RCI. Concentrate intake and RCI had low heritability. Genetic correlation between DMI and FIC was 0.98. Although the defined traits had moderate phenotypic correlations, the genetic correlations between DMI, FS, FIC, and RRI were above 0.79 (in absolute terms), suggesting that these traits are genetically similar. Therefore, selecting for FIC is expected to simply increase DMI and RRI, and there seems to be little advantage in separating concentrate and roughage intake in the genetic evaluation, because measured concentrate intake was determined by the feeding system in our data and not by the genetics of the cow.