A bedknife assembly for a reel mower cutting unit includes a cutting reel rotatably mounted to a frame, and a bedknife mounted to a bedknife support pivotally mounted to the frame in either a first position having a first pivot axis closer to the ground surface, or a second position having a second pivot axis further from the ground surface. The first pivot axis is further from the central axis of the cutting reel than the second pivot axis is from the central axis. The adjustable pivot axis may include a pair of eccentric pivot bushings mounted to the frame in either the first position or the second position. The adjustable pivot axis permits adjustment of the reel-to-bedknife gap after the reel is worn and its diameter is reduced, without dragging the bedknife on the turf, and extends the useful life of a cutting reel by increasing the adjustment range of the bedknife assembly.