Turbulent round buoyant jets discharging into linearly density-stratified stagnant fluids are studied. The sensitivity of the assumed entrainment relations and profile shapes in traditional integral models is explored. A different representation of the density profile is developed in order to more correctly represent the cross-sectional density distribution. In an experimental study, the dilution of a passive tracer along the jet trajectory, the maximum height of rise, and terminal dilution are measured. Measured center-line dilutions and jet widths are in essential agreement with model predictions with any of several previously proposed entrainment relations. It is found that jet mixing is not significantly influenced by either the ambient density gradient or the gravitational spreading layer from the jet collapse. There is some evidence of re-entrainment of jet fluid for horizontal nonbuoyant discharges. The integral model tends to under-predict the maximum height of jet rise and the associated dilution; this is apparently due to the inability to model the dynamics near that position correctly.