Nonlinear spiral vortices in fluid flow between counter-rotating cylinders are shown to induce an average axial pressure gradient when experiments are conducted between closed ends where the axial mean velocity must be zero. Previous calculations for spiral vortices have assumed periodic boundary conditions on the pressure, which in general is not compatible with zero mean axial velocity. Such calculations predicted wavespeeds which differed from experiment at leading nonlinear order, typically by 10% at 5% above criticality. In contrast, our numerical calculations with the constraint of zero mean axial flow agree well with the measured wavespeeds in the weakly nonlinear regime. Our results suggest a minor modification of previous analyses could incorporate the new constraint: the periodicity of the pressure could be replaced by periodicity of the pressure gradient, chosen to yield zero axial mean flow.