Generating binary trees, in lexicographic order, has been studied before. In this paper, the same problem is considered with the additional constraint that the height is bounded by a given number. A level numbering of nodes is used to encode binary trees as sequences of numbers in a one-to-one manner. The authors show their algorithm generates these sequences in, essentially, lexicographic order using constant average time per tree. The paper is easy to read and uses elementary combinatorics.