Recent work on Cygnus X-2 strongly suggests that neutron star or black hole binaries survive highly super-Eddington mass transfer rates without undergoing common-envelope evolution. We suggest here that the accretion flows in such cases are radiation pressure-dominated versions of the "ADIOS" picture proposed by Blandford & Begelman, in which almost all the mass is expelled from large radii in the accretion disk. We estimate the maximum radius from which mass loss is likely to occur, and we show that common-envelope evolution is probably avoided in any binary in which a main-sequence donor transfers mass on a thermal timescale to a neutron star or black hole, even though the mass transfer rate may reach values of ~10-3 M☉ yr-1. This conclusion probably applies also to donors expanding across the Hertzsprung gap, provided that their envelopes are radiative. SS 433 may be an example of a system in this state.
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