A source code for N symbols can be represented by a codeword length sequence (1,2,,N). A binary code is compact if it satisfies = 1. Also we may assume that 1 1 2 N. In this paper, we show that these two constraints can be replaced by max i for 1 i N - 1. Using the latter characterization, we construct a tree T N representing all binary compact codes. In fact every leaf of T N represents a compact code and vice versa. This technique can also be used to generate all compact codes for a given (1,2,,k), k < N.