Abstract: A controlled-pressure multi-cylinder riser tensioner has a plurality of preferably six control-cylinder units (1) with proximal ends (2) attached pivotally to a bottom surface of an operational floor (3) and distal ends (5) attached pivotally to a riser-tensioner ring (6). Pressure lines (20, 38) in communication with opposite ends of the control cylinders lead to sources of pressure (46, 47, 48, 52, 53, 62, 63) that are separately controlled. Stroke length of the control-cylinder units is typically 50 feet. Projection of the control-cylinder units downwardly into a moon pool (9) avoids their obstruction of work space on an operational floor (3) of a vessel (4). Positioning pneumatic and hydraulic machinery (10) below deck with tubing leading to the control cylinders lowers center of gravity for marine stability. An over-capacity for tensioning the marine riser with a portion of the control cylinders inactive or incapacitated increases reliability.