A relative risk estimate which relates an exposure to risk of disease will tend to be estimated too close to unity if that exposure is subject to random measurement error or intra-subject variability. "Independent" relative risk estimates, for the effect of one exposure after adjusting for confounding exposures, may be biased in either direction, depending on the amount of measurement imprecision in the exposure of interest and in the confounders. We describe two methods which estimate the bias in multivariate relative risk estimates due to the effect of measurement imprecision in one or more of the exposure variables in the model. Results from the two methods are compared in an example involving HDL cholesterol, triglycerides and coronary heart disease. In this example, the degree of bias in relative risk estimates is shown to be highly dependent on the amount of measurement imprecision ascribed to the exposures. It is concluded that when two exposures are substantially correlated, and one or both is subject to sizeable measurement imprecision, a study in which exposures are measured only once will be inadequate for investigating the independent effect of the exposures. Where feasible, epidemiologists should seek study populations where the correlation between the exposures is smaller.