Methods, servo systems, and data storage drives follow the lateral shift excursions of longitudinal tape, for example, from flangeless tape guides. A servo sensor is configured to sense lateral position of a tape head with respect to longitudinal servo tracks of the tape, a fine actuator is configured to translate the head laterally, and a coarse actuator is configured to translate the fine actuator laterally. Position error is determined between the head and a desired position related to the servo track, and the fine actuator operated to translate the head laterally to reduce the position error. In the embodiment, lateral shift excursion is sensed from the position error, and the coarse actuator is positioned substantially at a midpoint of the lateral shift excursion. Thus, the fine actuator follows the lateral shift excursions, while the coarse actuator remains at the midpoint.