A common problem in environmental exposure assessment and toxicology is the occurrence of contaminant levels that fall below a laboratory’s ability for accurate measurement. Values below this limit of quantification are said to be left censored. A few examples include nitrates (Iowa) and toxic metals (Fint, MI) in the public water supply, arsenic and cadmium in food, and PCBs in air and food. Methods for dealing with left-censored outcome variates in linear regression are well established. In this talk we address the more challenging problem of performing linear regression when both the covariates and the outcome can be left censored. We’ll consider a few different likelihood approaches.