The objective was to identify, in primary prevention, patients whose “required risk reduction” (ReqRR) is greater than the “achievable risk reduction” (ARR) that cholesterol-lowering or antihypertensive medication could provide. Individualized estimates of 10-year coronary heart disease or stroke risk were derived for 66 hypercholesterolemic (HC) and 64 hypertensive (HT) patients without symptomatic cardiovascular disease. These estimates were used in trade-off tasks identifying each individual’s ReqRR. Then individual ARRs were estimated (in HC patients by assuming total cholesterol/high density lipoprotein ratio reductions to 5.0; in HT patients by assuming systolic blood pressure reductions to 120 mmHg). 12 (18%) HC and 12 (19%) HT subjects would refuse medication regardless of the risk reduction offered. Of the remaining patients, 15/54 (28%; 95% C.I.: 16-40%) HC and 19/52 (37%; 95% C.I.: 24-51%) HT subjects were “over-requirers,” in that their ReqRR/ARR ratio was 1.5. There may be a notable proportion of patients whose ReqRR is considerably greater than what is achievable, implying that decision aids may help individuals clarify preferences about accepting/refusing medication for the primary prevention of cardiovascular disease.