In 1980, Bondy proved that for an integer a -connected graph of order is traceable () or Hamiltonian () or Hamiltonian-connected () if the degree sum of every set of pairwise nonadjacent vertices is at least . This generalizes the well-known sufficient conditions of Dirac () and Ore (). The condition in Bondy鈥檚 Theorem is not tight for . We improve this sufficient degree condition and show the general tightness of this result.