Summary: We consider avoiding squares and overlaps over the natural numbers, using a greedy algorithm that chooses the least possible integer at each step; the word generated is lexicographically least among all such infinite words. In the case of avoiding squares, the word is 01020103\(\dots\), the familiar ruler function, and is generated by iterating a uniform morphism. The case of overlaps is more challenging. We give an explicitly defined morphism \(\varphi : \mathbb N^* \to \mathbb N^*\) that generates the lexicographically least infinite overlap-free word by iteration. Furthermore, we show that for all \(h,k\in \mathbb N\) with \(h\leq k\), the word \(\varphi ^{k - h}(h)\) is the lexicographically least overlap-free word starting with the letter \(h\) and ending with the letter \(k\), and give some of its symmetry properties.