A disk drive is disclosed wherein a BEMF speed error is measured during a BEMF spindle speed control mode, and a spindle control current is updated in response to the BEMF speed error to drive the disk at an operating speed. A reference time period (RTP) is calibrated, and a sinusoidal error in a wedge time period (WTP) due to eccentricity in the disk rotating is estimated to generate an eccentricity compensation value. After switching to a wedge spindle speed control mode, an actual WTP is detected and a wedge speed error is generated in response to the RTP, the detected actual WTP, and the eccentricity compensation value. The disk is then maintained at the operating speed by updating the spindle control current in response to the wedge speed error.