  Beginning with Devaney, several authors have studied transcendental entire
functions for which every point in the escaping set can be connected to
infinity by a curve in the escaping set. Such curves are often called Devaney
hairs. We show that, in many cases, every point in such a curve, apart from
possibly a finite endpoint of the curve, belongs to the fast escaping set. We
also give an example of a Devaney hair which lies in a logarithmic tract of a
transcendental entire function and contains no fast escaping points.
