Along the base of glaciers and ice sheets, the sliding of ice over till depends critically on water drainage. In locations where drainage occurs through Röthlisberger channels, the effective pressure along the base of the ice increases and can lead to a strengthening of the bed, which reduces glacier sliding. The formation of Röthlisberger channels depends on two competing effects: (1) melting from turbulent dissipation opens the channel walls and (2) creep flow driven by the weight of the overlying ice closes the channels radially inward. Variation in downstream ice velocity along the channel axis, referred to as an antiplane shear strain rate, decreases the effective viscosity. This softening of the ice increases creep closure velocities. In this way, even a modest addition of antiplane shear can double the size of the Röthlisberger channels for a fixed water pressure or allow channels of a fixed radius to operate at lower effective pressure, potentially decreasing the strength of the surrounding bed. Furthermore, we show that Röthlisberger channels can be deformed away from a circular cross section under applied antiplane shear. These results can have broad impacts on sliding velocities and potentially affect the total ice flux out of glaciers and ice streams.