Iron oxide nanotubes of 50-150 nm outer diameter and 2-20 nm wall thickness are prepared in ordered arrays. Atomic layer deposition (ALD) of Fe2O3 from the precursor iron(III) tert-butoxide at 130-180 degrees C yields very smooth coverage of the pore walls of anodic alumina templates, with thickness growth of 0.26(+/- 0.04) A per cycle. The reduced Fe3O4 tubes are hard ferromagnets, and variations of the wall thickness d(w) have marked consequences on the magnetic response of the tube arrays. For 50 nm outer diameter, tubes of d(w) = 13 nm yield the largest coercive field (H-c > 750 Oe), whereas lower coercivities are observed on both the thinner and thicker sides of this optimum.