  We build a Shannon orbit equivalence between the universal odometer and a
variety of rank-one systems. This is done in a unified manner, using what we
call flexible classes of rank-one transformations. Our main result is that
every flexible class contains an element which is Shannon orbit equivalent to
the universal odometer. Since a typical example of flexible class is $\{T\}$
when $T$ is an odometer, our work generalizes a recent result by Kerr and Li,
stating that every odometer is Shannon orbit equivalent to the universal
odometer. When the flexible class is a singleton, the rank-one transformation
given by the main result is explicit. This applies to odometers, Chacon's map
and irrational rotations for almost every angle. We also prove that strongly
mixing systems, or systems with a given eigenvalue form flexible classes. In
particular, strong mixing, rationality or irrationality of the eigenvalues are
not preserved under Shannon orbit equivalence.
