The binary radio pulsar PSR 0655+64 is shown to be an effective astrophysical laboratory for testing gravity theories that violate the strong equivalence principle (SEP). Its observed spin-down rate has been used by us recently to test one aspect of SEP violation: the variability of the gravitational constant with cosmic time. Here it is suggested that PSR 0655+64 has the characteristics required for testing another aspect of SEP violation: the emission of dipole gravitational radiation. The companion of PSR 0655+64 is a white dwarf with a specific binding energy much smaller than that of the neutron star