Garnet films can be given orthorhombic anisotropy by growing films with positive magnetostriction constants under compression on (110) ‐oriented substrates. The positive magnetostriction is achieved by the incorporation of Mn3+ions in (Gd,Lu)3Fe5O12films. In this way bubble films with a strong in‐plane anisotropy field are obtained. This in‐plane anisotropy increases the maximum velocity of the domain walls to at least 40 000 cm s−1. The domain‐wall mobility in these films is about 1500 cm s−1 Oe−1. The dependence of the domain‐wall velocity on the anisotropy and on the orientation of the domain wall in the film plane is shown.