Experiments and field observations have shown that there are at least two modes of behavior for river plumes. In many cases, the plume turns to the right (in the Northern Hemisphere) on leaving the river mouth and follows the direction of Kelvin-wave propagation. Alternatively, a “bulge” can form in the plume and a fraction of the outflow volume becomes trapped near the mouth. This paper discusses how bulge formation can be affected by the vorticity profile at the river mouth. Due to the image effect, regions of cyclonic vorticity tend to propagate rightwards, whereas regions of anticyclonic vorticity propagate leftward upon exit from the source. If an outflow consists of regions of cyclonic vorticity to the left of regions of anticyclonic vorticity, the two image effects are in competition. We explore this phenomenon using a quasi-geostrophic model with piecewise-constant potential vorticity, which allows the vorticity profile at the source to be set as part of the problem. We present analytic solutions valid in the source region and at the head of the plume and show that all of the outflow travels rightwards if and only if the region of cyclonic vorticity is dominant. The initial-value problem for the model is integrated numerically using the method of contour dynamics, and the full parameter space is explored. We find that if the cyclonic and anticyclonic contributions cancel, as in the experiments of Avicola and Huq (2003), then steady solutions are unstable and a bulge can form downstream of the river mouth.