  The existence of a nontrivial polynomially convex hull with every point a
one-point Gleason part and with no nonzero bounded point derivations is
established. This strengthens the \hbox{celebrated} result of Stolzenberg that
there exists a nontrivial polynomially convex hull that contains no analytic
discs. A doubly generated counterexample to the peak point conjecture is also
presented.
