A continuous-media or patterned-media disk drive with a low ratio of linear bit density in bits per inch (BPI) in the along-the-track direction to track density in tracks per inch (TPI) in the cross-track direction has a magnetoresistive read head with high cross-track spatial resolution. The read head is located between two magnetic shields, with the shields and read head formed on a side surface of the head carrier perpendicular to the carrier's disk-facing surface. The carrier is supported by the disk drive actuator with the side surface of the carrier oriented generally parallel to the data tracks. In this arrangement the high-spatial-resolution direction of the read head (the transverse direction perpendicular to the side surface on which the head is formed) is in the radial or cross-track direction.