Gene co-expression networks capture biological relationships between genes and are important tools in predicting gene function and understanding disease mechanisms. We show that technical and biological artifacts in gene expression data confound commonly used network reconstruction algorithms. We demonstrate theoretically, in simulation, and empirically, that principal component correction of gene expression measurements prior to network inference can reduce false discoveries. Using data from the GTEx project in multiple tissues, we show that this approach reduces false discoveries beyond correcting only for known confounders.