Recent Geotail and Cluster observations revealed that thin current sheets in the near-Earth tail may have a bifurcated structure. In some cases the electrons are found to dominate the current. We present a generalization of the Harris current sheet equilibrium, which reproduces these features. The model ion distribution contains an additional element, viz. the quasi-adiabatic invariant of the ion motion across the sheet, and assumes ion temperature anisotropy outside the sheet. Bifurcated current sheets appear in the case of small ion anisotropy with T⊥i > T∥i (pancake distributions). In the opposite case (cigar distributions) the model describes a single-peaked ion-dominated current sheet embedded in a thicker Harris sheet, which is more relevant to the outflow region of the collisionless reconnection pattern in the deHoffman-Teller frame.