Dairy profit selection indexes have increasingly incorporated one of the various measures of feed efficiency (FE) as a key component trait. Definitions of FE traits range from DMI to residual feed intake (RFI), noting that RFI is effectively DMI adjusted for various energy sink traits such as body weight (BW) and milk energy (MILKE). Other definitions of FE fall between these 2 extremes such as feed saved (FS), which combines RFI and the portion of DMI required to maintain BW. The use of different FE traits can create confusion as to how to meaningfully compare their heritabilities or estimated breeding values (EBV) and their corresponding accuracies, or even how to differentially incorporate these EBV into selection indexes. If RFI and FS are merely linear functions of DMI, BW, and MilkE with known genetic variances and covariances between the 3 traits, there is no need to directly compute RFI or FS phenotypes to determine their heritabilities, genetic correlations, EBV and their respective accuracies. We demonstrate how the estimated aggregate genetic merits and corresponding accuracies are invariant to the specification of a FE trait within a selection index. That is, economic weights for a selection index involving one particular measure of FE readily convert into the economic weights for a selection index involving a different measure of FE. We use these different specifications of FE to provide insight as to the impact of the degree of missingness (i.e., paucity of DMI or BW relative to milk yield records) on the EBV accuracies of the various derivative FE traits. We particularly highlight that the generally observed higher EBV accuracies for DMI, then for FS, and lastly for RFI are partly driven by the typically greater genetic relative to residual correlations between DMI with RFI and FS and by the higher genetic correlations of DMI with BW and MILKE. Finally, we advocate a genetic regression approach to deriving FS and RFI recognizing that genetic versus residual relationships between FE component traits may differ substantially from each other.