Does gravitational radiation change the eccentricity of binary orbits?

Do the eccentricity of a binary orbit change with change in the semimajor axis due to loss of orbital angular momentum by gravitational radiation?

For an object like Haley's comet, the periapsis speed isn't fast enough to emit noticeable gravitational radiation, so GW emission doesn't really affect the orbit. But this is why we expect most binary black hole (BBH) or neutron star systems in the LIGO band to have relatively small eccentricity. By the time the binary approaches merger the orbits have pretty well circularized. Fig 1 from this paper by Zevin, et al (2021) shows that very few BBHs will have eccentricity more than $$0.1$$ by the time their GW emission reaches $$10$$ Hz.