  In a recent article we introduced and studied conical energies. We used them
to prove three results: a characterization of rectifiable measures, a
characterization of sets with big pieces of Lipschitz graphs, and a sufficient
condition for boundedness of nice singular integral operators. In this note we
give two examples related to sharpness of these results. One of them is due to
Joyce and M\"{o}rters, the other is new and could be of independent interest as
an example of a relatively ugly set containing big pieces of Lipschitz graphs.
