  Given a combinatorial description $C$ of a polyhedron having $E$ edges, the
space of dihedral angles of all compact hyperbolic polyhedra that realize $C$
is generally not a convex subset of $\mathbb{R}^E$ \cite{DIAZ}. If $C$ has five
or more faces, Andreev's Theorem states that the corresponding space of
dihedral angles $A_C$ obtained by restricting to {\em non-obtuse} angles is a
convex polytope. In this paper we explain why Andreev did not consider
tetrahedra, the only polyhedra having fewer than five faces, by demonstrating
that the space of dihedral angles of compact hyperbolic tetrahedra, after
restricting to non-obtuse angles, is non-convex. Our proof provides a simple
example of the ``method of continuity'', the technique used in classification
theorems on polyhedra by Alexandrow \cite{ALEX}, Andreev \cite{AND}, and
Rivin-Hodgson \cite{RH}.
