  We present a general result giving us families of incomplete and boundedly
complete families of discrete distributions. For such families, the classes of
unbiased estimators of zero with finite variance and of parametric functions
which will have uniformly minimum variance unbiased estimators with finite
variance are explicitly characterized. The general result allows us to
construct a large number of families of incomplete and boundedly complete
families of discrete distributions. Several new examples of such families are
described.
