Shadowgraph profiles collected in the thermohaline staircase east of Barbados reveal nearly-horizontal banding—unlike the vertical banding that has been observed in other fingering-favorable parts of the ocean. A plausible interpretation of this optical microstructure is that vertical shear is tilting over fingers. This paper presents a model for shear-tilting of salt fingers. The Ri = 6 inertial wave shears observed in C-SALT would tilt over and damp out square planform (kx = ky) fingers so rapidly that they could not produce significant fluxes. Vertical sheets aligned with the shear (ky = 0) would behave like unsheared fingers if the shear was steady but oceanic shear is predominantly near-inertial so turns with time. Therefore, an across-sheet shear component will develop and initially-aligned sheets too will ultimately be tilted over. This happens slowly enough that sheets can grow to produce significant fluxes. When the growth of tilting sheets is limited by a critical inverse finger Richardson number, (∇ × V)2/N2 ∼ 3–16, the model produces microstructure and fluxes similar to those reported from C-SALT. However, this constraint does not explain the density ratio dependence in laboratory studies and numerical simulations. What constrains finger growth needs to be better understood.