Batch effects in single-cell RNA-seq data pose a significant challenge for comparative analyses across samples, individuals, and conditions. Although batch effect correction methods are routinely applied, data integration often leads to overcorrection and can result in the loss of biological variability. In this work we present STACAS, a batch correction method for scRNA-seq that leverages prior knowledge on cell types to preserve biological variability upon integration. Through an open-source benchmark, we show that semi-supervised STACAS outperforms state-of-the-art unsupervised methods, as well as supervised methods such as scANVI and scGen. STACAS scales well to large datasets and is robust to incomplete and imprecise input cell type labels, which are commonly encountered in real-life integration tasks. We argue that the incorporation of prior cell type information should be a common practice in single-cell data integration, and we provide a flexible framework for semi-supervised batch effect correction.