Previous observations have shown that during periods of steady magnetospheric convection (SMC) a large amount of magnetic flux crosses the plasma sheet (corresponding to similar to 10 degrees wide auroral oval at the nightside) and that the magnetic configuration in the midtail is relaxed (the current sheet is thick and contains enhanced B-Z). These signatures are typical for the substorm recovery phase. Using near-geostationary magnetic field data, magnetic field modeling, and a novel diagnostic technique (isotropic boundary algorithm), we show that in the near-Earth tail the magnetic configuration is very stretched during the SMC events. This stretching is caused by an intense, thin westward current. Because of the strongly depressed B-Z, there is a large radial gradient in the near-tail magnetic field. These signatures have been previously associated only with the substorm growth phase. Our results indicate that during the SMC periods the magnetic configuration is very peculiar, with co-existing thin near-Earth current sheet and thick midtail plasma sheet. The deep local minimum of the equatorial B-Z that develops at R similar to 12 R(E) is consistent with steady, adiabatic, Earthward convection in the midtail. These results impose constraints on the existing substorm theories, and call for an explanation of how such a stressed configuration can persist for such along time without tail current disruptions that occur at the end of a substorm growth phase.