Identification of confounding factors, evaluation of their influence on cause-effect associations, and the introduction of appropriate ways to account for these factors are important considerations in designing case-control studies. This paper presents designs useful for these purposes, after first providing a statistical definition of a confounding factor. Differences in the ability to identify and evaluate confounding factors and estimate disease risk between designs employing stratification (matching) and designs randomly sampling cases and controls are noted. Linear logistic models for the analysis of data from such designs are described and are shown to liberalize design requirements and to increase relative risk estimation efficiency. The methods are applied to data from a multiple factor investigation of lung cancer patients and controls.