  We reexamine the production of gravitational waves by bubble collisions
during a first-order phase transition. The spectrum of the gravitational
radiation is determined by numerical simulations using the "envelope
approximation". We find that the spectrum rises as f^3.0 for small frequencies
and decreases as f^-1.0 for high frequencies. Thus, the fall-off at high
frequencies is significantly slower than previously stated in the literature.
This result has direct impact on detection prospects for gravity waves
originating from a strong first-order electroweak phase transition at
space-based interferometers, such as LISA or BBO. In addition, we observe a
slight dependence of the peak frequency on the bubble wall velocity.
