We recover two-dimensional magnetic structures of small-scale flux ropes in the solar wind from WIND space-craft data by solving the plane Grad-Shafranov equation as a spatial initial value problem. The cross-sections of two recovered flux ropes show nested non-circular loops of transverse field lines rather than concentric circles. The expected helical structure is recovered, albeit with significant distortions from axial symmetry. The rope structures are self-consistent, non-force free, magnetohydrostatic equilibria. Their orientations are determined by a novel technique. ¿ 2001 American Geophysical Union