Jupiter's satellite Io produces a standing magnetospheric disturbance, variously called the Alfv¿n wing or the Io flux tube, which carries current away from the satellite along the magnetic field and downstream. The physics governing this phenomenon remains controversial. This paper generalizes previous analytic treatments to include effects of plasma compressibility. The nonlinear MHD equations are shown to be equivalent to a nonlinear second-order partial differential equation for a single scalar function of position in the plane transverse to the wing. This equation bears a strong resemblance to the velocity potential equation for two-dimensional compressible flow in an ideal fluid. In certain limits the resemblance is exact, which permits approximate analytic solutions of the fluid case to be used to explore the properties of the compressible magnetofluid. The derivation allows translational symmetry in any direction, unlike the Alfv¿n-wing model which requires symmetry along an Alfv¿n characteristic. The wing current is governed by an effective conductance that generalizes the Alfv¿n wing conductance but is flexible enough to maintain a constant value in regions with different plasma densities. Hence this formalism suggests how the local plasma can adjust to provide a continuous current along the wing, all the way from the dense torus, through the rarified high-latitude regions, to Jupiter's ionosphere.