  A group $G$ is said to have restricted centralizers if for each $g \in G$ the
centralizer $C_G(g)$ either is finite or has finite index in $G$. Shalev showed
that a profinite group with restricted centralizers is virtually abelian. We
take interest in profinite groups with restricted centralizers of uniform
commutators, that is, elements of the form $[x_1,\dots,x_k]$, where
$\pi(x_1)=\pi(x_2)=\dots=\pi(x_k)$. Here $\pi(x)$ denotes the set of prime
divisors of the order of $x\in G$. It is shown that such a group necessarily
has an open nilpotent subgroup. We use this result to deduce that $\gamma_k(G)$
is finite if and only if the cardinality of the set of uniform $k$-step
commutators in $G$ is less than $2^{\aleph_0}$
