  We study gravitational-wave production from bubble collisions in a cosmic
first-order phase transition, focusing on the possibility of model separation
by the bubble nucleation rate dependence of the resulting gravitational-wave
spectrum. By using the method of relating the spectrum with the two-point
correlator of the energy-momentum tensor $\left< T(x)T(y) \right>$, we first
write down analytic expressions for the spectrum with a Gaussian correction to
the commonly used nucleation rate, $\Gamma \propto e^{\beta t}\rightarrow
e^{\beta t-\gamma^2t^2}$, under the thin-wall and envelope approximations. Then
we quantitatively investigate how the spectrum changes with the size of the
Gaussian correction. It is found that the spectral shape shows ${\mathcal
O}(10)\%$ deviation from $\Gamma \propto e^{\beta t}$ case for some physically
motivated scenarios. We also briefly discuss detector sensitivities required to
distinguish different spectral shapes.
