The coalescence instability is a widely studied, two-dimensional magnetohydrodynamic process by which magnetic islands can merge at growth rates exceeding those of the resistive instability. We present three-dimensional numerical simulations which indicate that, under a broad range of conditions, the coalescence instability will not significantly affect the evolution of a magnetofluid because it is overwhelmed by three-dimensional dynamics. The new 3D unstable modes are ideal. They exhibit fast growth at short wavelengths, a desirable feature for transitioning to turbulence. At long times the system is dominated by structure aligned with the large scale magnetic field, contrary to what is expected as a result of coalescence.