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A superconducting wire (diameter, d) exposed to an AC longitudinal or transverse. magnetic field (amplitude, H(sub m)) experiences a hysteretic power loss, W(sub h). If a DC transport current (density, J) is next applied, extra dissipation is encountered as the current interacts with the moving mixed-state vortices. But if J and H(sub m) are sufficiently small, and J(sub c) and d sufficiently large it is possible for loss-free current to flow down the central core of the wire out of range of the oscillating field. In other words, H(sub m) should be less than some ''penetration value'', H*(J) = H*(l-j), where H* is the usual penetration field and j (equivalent to) J/J(sub c). The current-related dissipation, W(sub dyn), can be interpreted as taking place within a dynamic resistivity, (rho)(sub dyn). Below H*(J) the only dissipation is W(sub h); above it the dissipation is W(sub t) = W(sub h) + W(sub dyn). In the latter regime, as J increases W(sub h) decreases and W(sub dyn), increases. The result is a net increase in W(sub t) during which, as J approaches J(sub c), W(sub h) tends to zero and W(sub dyn) undergoes a smooth transition to the flux-flow (and eventually, normal) state. Some of these predictions have been confirmed in a series of studies of dynamic resistivity in two samples of high-(Tc) YBCO strand -- a low-J(sub c) braid and a high-J(sub c) monofilament -- passing DC transport currents in transverse AC fields with H(sub m)s of up to about 800 gauss. Also described are the results of hysteresis loss measurements, taken at J = 0 using vibrating-sample magnetometry.