This paper presents a lubrication-type analysis of the pressure gradient-driven flow in a contraction connecting two parallel plate (Poiseuille) flow regions for a Bingham fluid. The solution is complete in the streamfunction at lowest order in the slope of the contraction. I find a floating core on the downstream side of the contraction, growing to match the floating core in the downstream Poiseuille flow. This is unusual. In most contracting or distorting flows the necessary deviatoric shear requires yielding everywhere, accompanied by deviatoric normal stresses.