For rotationally inelastic HF–HF collisions we have determined fully quantum partial opacities and integral cross sections for the j1=0, j2=0→11, 02, and 22 transitions at total energies of 500, 1000, and 8000 cm−1 and the 11→02 transition at 1000 cm−1. The potential was obtained from a recent fit of an ab initio surface and consisted of a spherically symmetric component and an anisotropic term with dipole–dipole symmetry. The collision dynamics were treated using the recently developed decoupled l-dominant (DLD) and coupled-states (CS) methods as well as within the Born approximation (BA). Comparison with selected full close-coupling calculations indicates that the CS method is very accurate for processes where collisions at small impact parameter play a large role, while the DLD method is to be preferred when large parameter collisions make the major contribution. The BA is, unfortunately, consistently unreliable, overestimating cross sections by more than an order of magnitude except at high energy. Additionally, the BA does not predict correctly the relative ratio of the 11→02 to 11→00 cross sections.