  Let $G$ be a finite group. We show that the order of the subgroup generated
by coprime $\gamma_k$-commutators (respectively $\delta_k$-commutators) is
bounded in terms of the size of the set of coprime $\gamma_k$-commutators
(respectively $\delta_k$-commutators). This is in parallel with the classical
theorem due to Turner-Smith that the words $\gamma_k$ and $\delta_k$ are
concise.
