  We construct a singly generated subalgebra of ${\mathcal K}({\mathcal H})$
which is non-amenable, yet is boundedly approximately contractible. The example
embeds into a homogeneous von Neumann algebra. We also observe that there are
singly generated, biflat subalgebras of finite Type I von Neumann algebras,
which are not amenable (and hence are not isomorphic to C*-algebras). Such an
example can be used to show that a certain extension property for commutative
operator algebras, which is shown in arXiv:1012.4259 to follow from
amenability, does not necessarily imply amenability.
