We consider tolerance graphs as defined by Golumbic, Monma, and Trotter (1984). These authors proposed a conjecture which can be stated as follows: If H is a comparability graph, then its complement <inl uoi="B6TYW-45F5W05-X-1" alt-char="H" height="14" width="14"> is a tolerance graph if and only if it is a bounded tolerance graph. A result which supports this conjecture was obtained by one of us in his Diploma-Thesis (Hennig, 1988) where it was shown that, for a tree T, the following three conditions are equivalent: (i)<inl uoi="B6TYW-45F5W05-X-2" alt-char="T" height="14" width="11"> is a tolerance graph, (ii) <inl uoi="B6TYW-45F5W05-X-2" alt-char="T" height="14" width="11"> is a bounded tolerance graph, (iii) T does not contain T₃ as a subtree, where T₃ denotes the tree which consists of three paths of length 3 starting at a common vertex. It is the purpose of the present note to give a short proof of this result.