Stackless traversal is a technique to speed up range queries by avoiding usage of a stack during the tree traversal. One way to achieve that is to transform a given binary tree to store a left child and a skip-connection (also called an escape index). In general, this operation requires an additional tree traversal during the tree construction. For some tree structures, however, it is possible achieve the same result at a reduced cost. We propose one such algorithm for a GPU hierarchy construction algorithm proposed by Karras in [Karras, 2012]. Furthermore, we show that our algorithm also works with the improved algorithm proposed by Apetrei in [Apetrei, 2014], despite a different ordering of the internal nodes. We achieve that by modifying the Apetrei's algorithm to restore the original Karras' ordering of the internal nodes. Using the modified algorithm, we show how to construct a hierarchy suitable for a stackless traversal in a single bottom-up pass.