A rocking journal bearing is provided in a piston coupling mechanism of a two-stroke cycle engine. The bearing includes a sleeve and a wristpin constructed with two sets of eccentrically-disposed bearing surfaces which alternate in accepting a compressive load during an operational cycle of the bearing. The sleeve includes a network of grooves to transport oil to the bearing surfaces. Lubricating oil flow through the bearing is minimized by limiting provision of pressurized oil from the wristpin to the network of grooves to portions of the cycle when one or the other of the sets of bearing surfaces receives the compressive load.