  Affine Deligne-Lusztig varieties are analogs of Deligne-Lusztig varieties in
the context of an affine root system. We prove a conjecture stated in the paper
arXiv:0805.0045v4 by Haines, Kottwitz, Reuman, and the first named author,
about the question which affine Deligne-Lusztig varieties (for a split group
and a basic $\sigma$-conjugacy class) in the Iwahori case are non-empty. If the
underlying algebraic group is a classical group and the chosen basic
$\sigma$-conjugacy class is the class of $b=1$, we also prove the dimension
formula predicted in op. cit. in almost all cases.
