  We consider the importance of the second-order dissipative self force for
gravitational wave dephasing for an extreme or intermediate mass ratio system
moving along a quasi-circular Schwarzschild orbit. For the first-order self
force we use the fully relativistic force in the Lorenz gauge for eternally
circular geodesics. The second-order self force is modeled by its 3.5 post
Newtonian counterpart. We evolve the system using the osculating orbits method,
and obtain the gravitational waveforms, whose phase includes all the terms -
within our approximation (and using the self force along circular geodesics) -
that are independent of the system's mass ratio. The partial dephasing due to
the second-order dissipative self force is substantially smaller than that of
the first-order conservative self force, although they are both at the same
order in the mass ratio.
