  Measure-theoretic slow entropy is a more refined invariant than the classical
measure-theoretic entropy to characterize the complexity of dynamical systems
with subexponential growth rates of distinguishable orbit types. In this paper
we prove flexibility results for the values of upper and lower polynomial slow
entropy of rigid transformations as well as maps admitting a good cyclic
approximation. Moreover, we show that there cannot exist a general upper bound
on the lower measure-theoretic slow entropy for systems of finite rank.
