Prediction for Maximum Supercooling in <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mrow> <mml:mi>SU</mml:mi> <mml:mo stretchy="false">(</mml:mo> <mml:mi>N</mml:mi> <mml:mo stretchy="false">)</mml:mo> </mml:mrow> </

The thermal confinement phase transition in SU(N) Yang-Mills theory is first order for N≥3, with bounce action scaling as N^{2}. Remarkably, lattice data for the action include a small coefficient whose presence likely strongly alters the phase transition dynamics. We give evidence, utilizing insights from softly broken supersymmetric Yang-Mills models, that the small coefficient originates from a deconfined phase instability just below the critical temperature. We predict the maximum achievable supercooling in SU(N) theories to be a few percent, which can be tested on the lattice. We briefly discuss the potentially significant suppression of the associated cosmological gravitational wave signals.