Lagging exposure information is often undertaken to allow for a latency period in cumulative exposure-disease analyses. The authors first consider bias and confidence interval coverage when using the standard approaches of fitting models under several lag assumptions and selecting the lag that maximizes either the effect estimate or model goodness of fit. Next, they consider bias that occurs when the assumption that the latency period is a fixed constant does not hold. Expressions were derived for bias due to misspecification of lag assumptions, and simulations were conducted. Finally, the authors describe a method for joint estimation of parameters describing an exposure-response association and the latency distribution. Analyses of associations between cumulative asbestos exposure and lung cancer mortality among textile workers illustrate this approach. Selecting the lag that maximizes the effect estimate may lead to bias away from the null; selecting the lag that maximizes model goodness of fit may lead to confidence intervals that are too narrow. These problems tend to increase as the within-person exposure variation diminishes. Lagging exposure assignment by a constant will lead to bias toward the null if the distribution of latency periods is not a fixed constant. Direct estimation of latency periods can minimize bias and improve confidence interval coverage.