  We classify the complete hyperbolic 3-manifolds admitting a maximal cusp of
volume at most 2.62. We use this to show that the figure-8 knot complement is
the unique 1-cusped hyperbolic 3-manifold with nine or more non-hyperbolic
fillings; to show that the figure-8 knot complement and its sister are the
unique hyperbolic 3-manifolds with minimal volume maximal cusps; and to extend
results on determining low volume closed and cusped hyperbolic 3-manifolds.
