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,

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... hose 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.