Biological differences of interest in large, high-dimensional flow cytometry datasets are often obscured by undesired variations caused by differences in cytometers, reagents, or operators. Each variation type requires a different correction strategy, and their unknown contributions to overall variability hinder automated correction. We now describe swiftReg, an automated method that reduces undesired sources of variability between samples and particularly between batches. A high-resolution cluster map representing the multidimensional data is generated using the SWIFT algorithm, and shifts in cluster positions between samples are measured. Subpopulations are aligned between samples by displacing cell parameter values according to registration vectors derived from independent or locally-averaged cluster shifts. Batch variation is addressed by registering batch control or consensus samples, and applying the resulting shifts to individual samples. swiftReg selectively reduces batch variation, enhancing detection of biological differences. swiftReg outputs registered datasets as standard .FCS files to facilitate further analysis by other tools.