A homeomorphism is quasi-symmetric if there exist such that for every and , . In this paper we demonstrate a topological condition that prohibits a tent-map to be quasi-symmetrically conjugate to any unimodal map. This topological condition is so weak that almost every tent-map satisfies it. We show in a similar way that typically a degree 2 circle map with a critical point cannot be quasi-symmetrically conjugate to the angle doubling map. We discuss another topological condition (persistent recurrence of the critical point), which is almost complementary to the first. We show that a unimodal map f with a persistently recurrent critical point does not satisfy the Collet - Eckmann condition and (if f is non-flat as well), is not quasi-symmetrically conjugate to a tent-map.