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Studies concerned with measuring values and preferences for health states and health status components have typically employed "direct" scaling techniques that require conclusions to be based on definition. Problems and limitations of direct scaling are discussed. The algebraic modeling approach is new to health services research; it emphasizes testing models of how respondents combine stimulus information. The model specifies the causal relationship between the stimulus information and the responses. Subjective stimulus and response scales are derived from the model when the data satisfy the model's predictions. Thus, the validity of the subjective scale values rests on the validity of the model. In the present research, university students judged preferences between health states, each described by a physical (degree of physical activity) and mental (level of happiness/depression) component. The object of the research was to determine the subjective trade-offs between physical and mental health values in these preference judgments. For all respondents, preference judgments were consistent with the predictions of a preference model that yielded interval scales of the health states. Also, there were systematic interactions between physical and mental values, so that when a health state was bad on one component (e.g., poor physical health), the other component had less of an effect. However, results revealed individual differences in emphasis placed on the physical and mental health components. Advantages of replacing presently used measurement techniques with the algebraic modeling approach in general population studies are discussed.