Methods of controlling seeking of a transducer that is adjacent to a rotatable disk in a disk drive include determining an expected seek time associated with moving the transducer from an initial track to a target track on the disk. An expected rotational latency time is determined which is associated with rotating the disk to move an addressed data block on the target track adjacent to the transducer after the transducer would be expected to arrive at the target track. A scaled velocity limit is determined which is based on the expected seek time and the expected rotational latency time. While seeking the transducer from the initial track to the target track, the radial velocity of the transducer relative to the disk is regulated in response to the scaled velocity limit. Related apparatus for controlling seeking of a transducer are also described.