Two factorial design experiments were carried out in the spring of 1994 and 1995, each of 6 weeks, to quantify the effects of sward height (SH), concentrate level (CL) and initial milk yield (IMY) on milk production and grazing behaviour of continuously stocked dairy cows. In Experiment 1, forty‐five Holstein Friesian cows were in five groups with initial milk yields of 16·9, 21·1, 28·0, 31·5 and 35·5 kg d–1, grazed sward heights were 3–5, 5–7 and 7–9 cm (LSH, MSH and HSH respectively), and concentrates were fed at rates of 0, 3 and 6 kg d–1. In Experiment 2, 48 cows were in two groups with IMY of 21·3 and 35·5 kg d–1, grazed sward heights were 3–5 and 7–9 cm (LSH and HSH), and concentrates were fed at 0 and 6 kg d–1 and ad libitum. Multiple regression models were used to quantify the effects of the three variables on milk yield persistency (MYP), estimated herbage dry‐matter (DM) intake (HDMI), grazing time (GT) and rate of DM intake (RI). The partial regression coefficients showed that increased SH led to increased MYP (Experiment 1 P < 0·001, Experiment 2 P < 0·05), increased HDMI (P < 0·01, P < 0·01), increased GT (P < 0·001, P < 0·05) and increased RI (P < 0·001, P < 0·05). Increasing CL led to increased MYP (NS, P < 0·001), decreased HDMI (P < 0·001, P < 0·001), decreased GT (NS, P < 0·001) and decreased RI (P < 0·001, P < 0·001). Higher IMY level of cows decreased MYP (P < 0·001, P < 0·001), increased HDMI (P < 0·001, P < 0·001), increased GT (P < 0·001, P < 0·05) and increased RI (P < 0·05, P < 0·01). The models were highly significant (P < 0·001), and accounted for 0·48–0·87 of the total variance. The partial regression coefficients quantified the extent to which GT and RI by cows respond positively to higher IMY, and negatively to increased CL, but respond differently (GT declines in response to a higher RI) with increasing SH.