  We study production of gravitational waves (GWs) in strongly supercooled
cosmological phase transitions in gauge theories. We extract from two-bubble
lattice simulations the scaling of the GW source, and use it in many-bubble
simulations in the thin-wall limit to estimate the resulting GW spectrum. We
find that in presence of the gauge field the GW source decays with bubble
radius as $\propto R^{-3}$ after collisions. This leads to a GW spectrum that
follows $\Omega_{\rm GW} \propto \omega^{2.3}$ at low frequencies and
$\Omega_{\rm GW} \propto \omega^{-2.4}$ at high frequencies, marking a
significant deviation from the popular envelope approximation.
