Let X be a compactum in En of dimension at most n – 2. In [9, Theorem 4.1] it was shown that there is an arbitrarily small homeomorphism h of En fixed outside any given neighborhood of X, so that h(X) has vertical order n – 1 provided n ≠ 3. If X is a 0-dimensional set or a tame 1-dimensional set in E3 then the result is still true. However, the examples of tangled continua of Bothe [2] and McMillan and Row [7] are not amenable to the techniques used in dimensions other than three. This prompted Wright [9] to make the following conjecture.