We re-examine 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 and BBO. In addition, we observe a slight dependence of the peak frequency on the bubble wall velocity.