  Unbiased location- and scale-invariant `elemental' estimators for the GPD
tail parameter are constructed. Each involves three log-spacings. The
estimators are unbiased for finite sample sizes, even as small as N=3. It is
shown that the elementals form a complete basis for unbiased location- and
scale-invariant estimators constructed from linear combinations of
log-spacings. Preliminary numerical evidence is presented which suggests that
elemental combinations can be constructed which are consistent estimators of
the tail parameter for samples drawn from the pure GPD family.
