Statistical methods for cost-effectiveness analysis (CEA) for two treatments that mimic the deterministic optimal rules of CEA are presented. In these rules the objective is to determine the treatment with the maximal effectiveness whose unit cost is less than an amount, λ, that a decision-maker is willing to pay (WTP). This is accomplished by identifying the treatment with the largest positive net health benefit (NHB), which is a function of λ, while controlling the familywise error rate both when the WTP value is given and when it is unspecified. Fieller's theorem is used to determine a region of WTP values where the NHBs of the treatments are not distinguishable. For each λ outside of the confidence region, the larger treatment is identified. A newly developed one-tailed analogue of Fieller's theorem is used to determine the WTP values where a treatment's NHB is positive. The situation in which both treatments are experimental is distinguished from the case where one of the treatments is usual care. The one-tailed confidence region is used in the latter case to obtain the λ values where the NHBs are not different, and determining the region of positivity of the NHBs may be unnecessary. An example is presented in which the cost-effectiveness of two antipsychotic treatments is evaluated. Copyright © 2001 John Wiley & Sons, Ltd.