  By the method of rho-integration we obtain all Lanczos potentials L_{ABCA'}
of the Weyl spinor that, in a certain sense, are aligned to a geodesic
shear-free expanding null congruence. We also obtain all spinors
H_{ABA'B'}=Q_{AB}o_{A'}o_{B'}, Q_{AB}=Q_{(AB)} satisfying
nabla_{(A}{}^{B'}H_{BC)A'B'}=L_{ABCA'}. We go on to prove that H_{ABA'B'} can
be chosen so that Gamma_{ABCA'}=nabla_{(A}{}^{B'} H_{B)CA'B'} defines a metric
asymmetric curvature-free connection such that L_{ABCA'}=Gamma_{(ABC)A'} is a
Lanczos potential that is aligned to the geodesic shear-free expanding
congruence. These results are a generalization to a large class of
algebraically special spacetimes (including all vacuum ones for which the
principal null direction is expanding) of the curvature-free connection of the
Kerr spacetime found by Bergqvist and Ludvigsen, which was used in a
construction of quasi-local momentum.
