<p>In this article, we present a method to construct <i>e</i>-power <i>b</i>-happy numbers of any height. Using this method, we construct a tree that encodes these happy numbers, their heights, and their ancestry—relation to other happy numbers. For fixed power <i>e</i> and base <i>b</i>, we consider happy numbers with at most <i>k</i> digits and we give a formula for the cardinality of the preimage of a single iteration of the happy function. We show that these happy numbers arise naturally as children of a given vertex in the tree. We conclude by applying this technique to <i>e</i>-power <i>b</i>-unhappy numbers of a given height.</p>