Experiments document the influence of flow on the Plateau–Rayleigh (PR) instability of a near-cylindrical liquid bridge. The slightly heavy bridge is subjected to a surrounding pipe flow from bottom to top. Linear and nonlinear regimes of response are reported. Islands of stability in flow rate are observed; that is, there are bridges that are stable with flow but otherwise not. Density imbalance and flow each, on its own, is destabilizing but together they are stabilizing as recorded by a variety of measures. This nonlinear stabilization is explained in terms of the codimension-2 nature of the pitchfork bifurcation of the ‘perfect’ Plateau–Rayleigh instability.