Current approaches to single-cell transcriptomic analysis are computationally intensive and require assay-specific modeling, which limits their scope and generality. We propose a novel method that compares and clusters cells based on their transcript-compatibility read counts rather than on the transcript or gene quantifications used in standard analysis pipelines. In the reanalysis of two landmark yet disparate single-cell RNA-seq datasets, we show that our method is up to two orders of magnitude faster than previous approaches, provides accurate and in some cases improved results, and is directly applicable to data from a wide variety of assays.