  The known static electro-vacuum black holes in a globally AdS$_4$ background
have an event horizon which is geometrically a round sphere. In this work we
argue that the situation is different in models with matter fields possessing
an explicit dependence on the azimuthal angle $\varphi$, which, however, does
not manifest at the level of the energy-momentum tensor. As a result, the full
solutions are axially symmetric only, possessing a single (timelike) Killing
vector field. Explicit examples of such static black holes are constructed in
Einstein--(complex) scalar field and Einstein--Yang-Mills theories. The basic
properties of these solutions are discussed, looking for generic features. For
example, we notice that the horizon has an oblate spheroidal shape for
solutions with a scalar field and a prolate one for black holes with Yang-Mills
fields. The deviation from sphericity of the horizon geometry manifests itself
in the holographic stress-tensor. Finally, based on the results obtained in the
probe limit, we conjecture the existence in the Einstein-Maxwell theory of
static black holes with axial symmetry only.
