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We study the orbital evolution of a radiation-damped binary in the extrememass ratio limit, and the resulting waveforms, to one order beyond what can beobtained using the conservation laws approach. The equations of motion aresolved perturbatively in the mass ratio (or the corresponding parameter in thescalar field toy model), using the self force, for quasi-circular orbits arounda Schwarzschild black hole. This approach is applied for the scalar model.Higher-order corrections yield a phase shift which, if included, may makegravitational-wave astronomy potentially highly accurate.Comment: 4 pages, 3 Encapsulated PostScript figure

Orbital evolution of a test particle around a black hole: Higher-order corrections