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Integration of single-cell RNA-sequencing (scRNA-seq) datasets is standard in scRNA-seq analysis. Nevertheless, current computational methods struggle to harmonize datasets across systems such as species, organoids and primary tissue, or different scRNA-seq protocols, including single-cell and single-nuclei. Conditional variational autoencoders (cVAE) are a popular integration method, however, existing strategies for stronger batch correction have limitations. Increasing the Kullback-Leibler divergence regularization does not improve integration and adversarial learning removes biological signals. Here, we propose sysVI, a cVAE-based method employing VampPrior and cycle-consistency constraints. We show that sysVI integrates across systems and improves biological signals for downstream interpretation of cell states and conditions.