  We show that previously known non-asymptotically flat static black hole
solutions of Einstein-Maxwell-dilaton theory may be obtained as near-horizon
limits of asymptotically flat black holes. Specializing to the case of the
dilaton coupling constant $\alpha^2 = 3$, we generate from the
non-asymptotically flat magnetostatic or electrostatic black holes two classes
of rotating dyonic black hole solutions. The rotating dyonic black holes of the
``magnetic'' class are dimensional reductions of the five-dimensional
Myers-Perry black holes relative to one of the azimuthal angles, while those of
the ``electric'' class are twisted dimensional reductions of rotating dyonic
Rasheed black strings. We compute the quasi-local mass and angular momentum of
our rotating dyonic black holes, and show that they satisfy the first law of
black hole thermodynamics, as well as a generalized Smarr formula. We also
discuss the construction of non-asymptotically flat multi-extreme black hole
configurations.
