Motivation: A major challenge in utilizing microarray technologies to measure nucleic acid abundances is normalization, the goal of which is to separate biologically meaningful signal from other confounding sources of signal, often due to unavoidable technical factors. It is intuitively clear that true biological signal and confounding factors need to be simultaneously considered when performing normalization. However, the most popular normalization approaches do not utilize what is known about the study, both in terms of the biological variables of interest and the known technical factors in the study, such as batch or array processing date. Results: We show here that failing to include all study-specific biological and technical variables when performing normalization leads to biased downstream analyses. We propose a general normalization framework that fits a study-specific model employing every known variable that is relevant to the expression study. The proposed method is generally applicable to the full range of existing probe designs, as well as to both single-channel and dual-channel arrays. We show through real and simulated examples that the method has favorable operating characteristics in comparison to some of the most highly used normalization methods.