Given a multiset M = V(1) boolean OR V(2) U ... U V(C) of n elements and a capacity function Delta : [1, C] -> [2, n - 1], we consider the problem of enumerating all unrooted trees T on M such that the degree of each vertex v is an element of V(i) is bounded from above by Delta(i). The problem has a direct application of enumerating isomers of tree-like chemical graphs. We give an algorithm that generates all such trees without duplication in O(1)-time delay per output in the worst case using O(n) space, with O(n) initial preprocessing time.