Novel designs and procedures have been developed which greatly reduce the end effects in a concentric cylinder viscometer. The essential features of the most versatile design are a hollow inner cylinder, open at both ends, conterminous inner and outer cylinders, and a pool of mercury at the bottom of the cup which essentially eliminates the torque exerted on the bottom of the inner cylinder and on the sample in the gap. Preliminary experiments with a Newtonian liquid and a suboptimal design demonstrate that absolute measurements can be made, provided the curved sample/air and sample/mercury interfaces are “symmetrical” across the top and bottom of the gap. The method promises to be particularly suitable for rather viscous, non‐Newtonian fluids, including those with an appreciable yield stress. Existing viscometers can be readily modified to implement these ideas. The limitations are that the fluid to be tested must be considerably more viscous than mercury, and the angular velocity of the cup must be kept below levels where centrifugal forces or normal stress effects start to significantly affect the shape of the sample/air and sample/mercury interfaces.