Mesh stabilization techniques for controlling the hourglass modes in underintegrated hexahedral and quadrilateral elements are examined. It is shown, using the Laplace equation as a model, that the 'orthogonal' hourglass techniques previously developed can be obtained from simple requirements that ensure that the finite element patch test is also satisfied. By contrast, other hourglass control techniques fail to satisfy the patch test for elements that are not rectangular. These results also apply to certain finite difference methods. The extension of these techniques to solid mechanics problems is also discussed.