Divergence-time estimation based on molecular phylogenies and the fossil record has provided insights into fundamental questions of evolutionary biology. In Bayesian node dating, phylogenies are commonly time calibrated through the specification of calibration densities on nodes representing clades with known fossil occurrences. Unfortunately, the optimal shape of these calibration densities is usually unknown and they are therefore often chosen arbitrarily, which directly impacts the reliability of the resulting age estimates. As possible solutions to this problem, two non-exclusive alternative approaches have recently been developed, the “fossilized birth-death” model and “total-evidence dating”. While these approaches have been shown to perform well under certain conditions, they require including all (or a random subset) of the fossils of each clade in the analysis, rather than just relying on the oldest fossils of clades. In addition, both approaches assume that fossil records of different clades in the phylogeny are all the product of the same underlying fossil sampling rate, even though this rate has been shown to differ strongly between higher-level taxa. We here develop a flexible new approach to Bayesian node dating that combines advantages of traditional node dating and the fossilized birth-death model. In our new approach, calibration densities are defined on the basis of first fossil occurrences and sampling rate estimates that can be specified separately for all clades. We verify our approach with a large number of simulated datasets, and compare its performance to that of the fossilized birth death model. We find that our approach produces reliable age estimates that are robust to model violation, on par with the fossilized birth-death model. By applying our approach to a large dataset including sequence data from over 1000 species of teleost fishes as well as 147 carefully selected fossil constraints, we recover a timeline of teleost diversification that is incompatible with previously assumed vicariant divergences of freshwater fishes. Our results instead provide strong evidence for trans-oceanic dispersal of cichlids and other groups of teleost fishes.