Rote words are infinite words that contain $2n$ factors of length $n$ for every $n \geq 1$. Shallit and Shur, as well as Ollinger and Shallit, showed that there are Rote words that avoid $(5/2)^+$-powers and that this is best possible. In this note we give a structure theorem for the Rote words that avoid $(5/2)^+$-powers, confirming a conjecture of Ollinger and Shallit.