  Observations of gravitational waves from inspiralling compact binaries using
laser-interferometric detectors can provide accurate measures of parameters of
the source. They can also constrain alternative gravitation theories. We
analyse inspiralling compact %binaries in the context of the scalar-tensor
theory of Jordan, Fierz, Brans and Dicke, focussing on the effect on the
inspiral of energy lost to dipole gravitational radiation, whose source is the
gravitational self-binding energy of the inspiralling bodies. Using a
matched-filter analysis we obtain a bound on the coupling constant $\omega_{\rm
BD}$ of Brans-Dicke theory. For a neutron-star/black-hole binary, we find that
the bound could exceed the current bound of $\omega_{\rm BD}>500$ from
solar-system experiments, for sufficiently low-mass systems. For a $0.7
M_\odot$ neutron star and a $3 M_\odot$ black hole we find that a bound
$\omega_{\rm BD} \approx 2000$ is achievable. The bound decreases with
increasing black-hole mass. For binaries consisting of two neutron stars, the
bound is less than 500 unless the stars' masses differ by more than about $0.5
M_\odot$. For two black holes, the behavior of the inspiralling binary is
observationally indistinguishable from its behavior in general relativity.
These bounds assume reasonable neutron-star equations of state and a detector
signal-to-noise ratio of 10.
