A careful numerical analysis of a measured steady-state I-V (current-voltage) characteristic of a superconducting compound conductor with very fine strands is reported. The actual, nonlinear heat transfer from copper to the helium bath is considered. It is shown that in the current-sharing state the flux flow resistance of the superconductor, Rf, increases from zero to values much greater than the copper resistance, RCu. For Rf∼RCu, the superconductor current Is is a function of the field H, the voltage V, and the temperature T. For Rf»RCu, Is is a function of H, independent of V, and a linear function of T. The value of this function extrapolated to the bath temperature Tb is appreciably greater than the critical current. In the absence of flux jumps, the current-sharing state should be terminated by the steady-state condition dI/dV = 0. The actual ``take off'' (sudden transition into the normal state) observed, however, took place below the mentioned steady-state limit and before the transition from nucleate to film boiling. The new findings on the steady-state performance of compound conductors with very thin strands make essential modifications of the usual theoretical approaches necessary. It is shown how the new approach can be applied to compound conductors with thick filaments.