A computer input device uses a standard mouse design and includes at least one thumb wheel or roller to provide three-dimensional cursor positioning. Left and right rollers, for use by left- and right-handed users, protrude from left and right sides of a standard mouse. The left and right rollers are axially mounted on left and right drive shafts that extend axially through left and right encoder wheels, respectively. Each encoder wheel forms part of a transducer for producing signals indicating movement or rotation of the wheel. These signals can be used for calculating cursor movement or for various other purposes in computer software applications. Alternatively, the rollers are coupled to switches or a single roller protrudes from the top of the mouse.