The multispecies coalescent (MSC) reconstructs species trees from a set of genes, and fully Bayesian MSC methods like *BEAST estimate species trees from multiple sequence alignments. Today thousands of genes can be sequenced for a given study, but using that many genes with *BEAST is intractably slow. One alternative is concatenation, which assumes that the evolutionary history of each gene tree is identical to the species tree. This is an inconsistent estimator of species tree topology, and a worse estimator of divergence times. Concatenation also induces spurious substitution rate variation when incomplete lineage sorting is present. Another alternative is to use summary MSC methods like ASTRAL, but such methods are also unsatisfactory because they infer branch lengths in coalescent units, and so cannot estimate divergence times. To enable fuller use of available data and more accurate inference of species tree topologies, divergence times, and substitution rates, we have developed a new version of *BEAST called StarBEAST2. To improve convergence rates we add analytical integration of population sizes and novel MCMC operators which improved computational performance by 3.1x when analyzing a single empirical data set, and an average of 6.2x across 96 simulated data sets. Convergence rates are also more consistent between chains than *BEAST. To enable accurate estimates of per-species substitution rates we introduce species tree relaxed clocks, and show that StarBEAST2 is a more powerful and robust estimator of rate variation than concatenation. StarBEAST2 is available through the BEAUTi package manager in BEAST 2.4 and above.