Increasing genetic merit for production has been associated with a decline in dairy cow fertility. In order to sustain lactation it appears that appreciable amounts of body condition are being mobilised, which may impinge on fertility. Body condition score (BCS) of first lactation heifers is recorded by Holstein UK and Ireland (HUKI) as part of its national type classification scheme. BCS may be a useful selection criterion for improving fertility. Calving dates and hence calving interval (CI) are generally very reliably recorded, but the usefulness of CI as a selection criterion is hampered for a number of reasons, one being that only the most fertile cows have two consecutive calving dates. This is a serious issue that still needs to be addressed. Our aim here was to investigate if there is genetic covariation between BCS and CI after adjustment for milk yield and to investigate selection responses in all three traits when selection is for each trait in turn and how responses are affected by restrictions imposing no genetic change in one of the traits. Restricting a trait to no change when it is correlated to a trait under selection may be important in developing customised indexes to satisfy specific requirements.