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We study gravitational wave (GW) production in strongly supercooled cosmological phase transitions, taking particular care of models featuring a complex scalar field with a U(1) symmetric potential. We perform lattice simulations of two-bubble collisions to properly model the scalar field gradients, and compute the GW spectrum sourced by them using the thin-wall approximation in many-bubble simulations. We find that in the U(1) symmetric case the low-frequency spectrum is $$\propto \omega $$ ∝doi:10.1140/epjc/s10052-020-08589-1 fatcat:hqpxvywklrde7lkm23zzo4ophe