MOTIVATION: Quantification estimates of gene expression from single-cell RNA-seq (scRNA-seq) data have inherent uncertainty due to reads that map to multiple genes. Many existing scRNA-seq quantification pipelines ignore multi-mapping reads and therefore underestimate expected read counts for many genes. alevin accounts for multi-mapping reads and allows for the generation of 'inferential replicates', which reflect quantification uncertainty. Previous methods have shown improved performance when incorporating these replicates into statistical analyses, but storage and use of these replicates increases computation time and memory requirements. RESULTS: We demonstrate that storing only the mean and variance from a set of inferential replicates ('compression') is sufficient to capture gene-level quantification uncertainty, while reducing disk storage to as low as 9% of original storage, and memory usage when loading data to as low as 6%. Using these values, we generate 'pseudo-inferential' replicates from a negative binomial distribution and propose a general procedure for incorporating these replicates into a proposed statistical testing framework. When applying this procedure to trajectory-based differential expression analyses, we show false positives are reduced by more than a third for genes with high levels of quantification uncertainty. We additionally extend the Swish method to incorporate pseudo-inferential replicates and demonstrate improvements in computation time and memory usage without any loss in performance. Lastly, we show that discarding multi-mapping reads can result in significant underestimation of counts for functionally important genes in a real dataset. AVAILABILITY AND IMPLEMENTATION: makeInfReps and splitSwish are implemented in the R/Bioconductor fishpond package available at https://bioconductor.org/packages/fishpond. Analyses and simulated datasets can be found in the paper's GitHub repo at https://github.com/skvanburen/scUncertaintyPaperCode. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.