  We provide a Laakso construction to prove that the property of having an
equivalent norm with the property $(\beta)$ of Rolewicz is qualitatively
preserved via surjective uniform quotient mappings between separable Banach
spaces. On the other hand, we show that the $(\beta)$-modulus is not
quantitatively preserved via such a map by exhibiting two uniformly
homeomorphic Banach spaces that do not have $(\beta)$-moduli of the same
power-type even under renorming.
