While RNA-Seq has enabled great progress towards the goal of wide-scale isoform-level mRNA quantification, short reads have limitations when resolving complex or similar sets of isoforms. As a result, estimates of isoform abundance carry far more uncertainty than those made at the gene level. When confronted with this uncertainty, commonly used methods produce estimates that are often high-variance---small perturbations in the data often produce dramatically different results, confounding downstream analysis. We introduce a new method, Isolator, which analyzes all samples in an experiment in unison using a simple Bayesian hierarchical model. Combined with aggressive bias correction, it produces estimates that are simultaneously accurate and show high agreement between samples. In a comprehensive comparison of accuracy and variance, we show that this property is unique to Isolator. We further demonstrate that the approach of modeling an entire experiment enables new analyses, which we demonstrate by examining splicing monotonicity across several time points in the development of human cardiomyocyte cells.