First, we present a two-fold double copy for classical radiation from spinless sources. We compute, to the leading order in perturbation theory, the scalar radiation generated by a system of bi-adjoint point charges coupled to a bi-adjoint scalar field. A set of color-to-kinematic substitution rules transform the scalar radiation to Yang-Mills radiation from a system of adjoint color charges, while a second application of the same rules gives radiation in a gravitational theory with point masses. 

  Next, we extend the classical double copy to spinning sources, thus bringing it closer to the astrophysically relevant case of compact binaries. Here, we compute, to linear order in spin, Yang-Mills radiation generated by a system of spinning color charges with chromomagnetic spin dipole couplings. The color-to-kinematic substitution rules then yield radiation in a theory with spinning sources coupled to the graviton, dilaton and a 2-form gauge field. If this classical double copy correspondence persists to higher orders in perturbation theory, it suggests the possibility of vastly simplifying the calculation of gravitational radiation, in particular, that from colliding compact objects.