  We consider banana shaped regions as examples of compact regions, whose
boundary has two conical singularities. Their regularised holographic entropy
is calculated with all divergent as well as finite terms. The coefficient of
the squared logarithmic divergence, also in such a case with internally curved
boundary, agrees with that calculated in the literature for infinite circular
cones with their internally flat boundary. For the otherwise conformally
invariant coefficient of the ordinary logarithmic divergence an anomaly under
exceptional conformal transformations is observed.
  The construction of minimal submanifolds, needed for the entanglement entropy
of cones, requires fine-tuning of Cauchy data. Perturbations of such
fine-tuning leads to solutions relevant for hollow cones. The divergent parts
for the entanglement entropy of hollow cones are calculated. Increasing the
difference between the opening angles of their outer and inner boundary, one
finds a transition between connected solutions for small differences to
disconnected solutions for larger ones.
