An analytic approach, based on thin-wall theory, to analysis of the "controlled clearance" method bf restricting the gap between a shaft and a surrounding cylinder is presented. A modified form of thin-wall theory allows this analysis to be extended to seals with outside to inside diameter ratios up to 2,3. The effects of (a) the supply pressure, the jacket pressure, the pressure dependence of the viscosity of the oil and the geometry of the system on (b) the deformation of the cylinder, the pressure profile in the gap between the shaft and the cylinder and the flow of oil are illustrated. A path using this information is given for the design of a controlled clearance seal. It is shown that when the jacket pressure and the supply pressure are equal (reentrant cylinder condition) the supply pressure needed to close the gap is infinite. The difference between this result and that for a cylinder with a built-in end, for which the supply pressure for closure is finite, is discussed. Experimental tests are described and the results are shown to agree with computed figures based on the theory. This work is of particular relevance to hydraulically actuated standards of pressure and force, where "simple" piston-cylinder assemblies suffer excessive deformations at pressures beyond 50 MPa.