  In 1954 B. H. Neumann discovered that if G is a group in which all conjugacy
classes are finite with bounded size, then the derived group G' is finite.
Later (in 1957) Wiegold found an explicit bound for the order of G'. We study
groups in which the conjugacy classes containing commutators are finite with
bounded size. We obtain the following results.
  Let G be a group and n a positive integer.
  If |x^G|<n for any commutator x in G, then the second derived group G" is
finite with n-bounded order.
  If |x^{G'}|<n for any commutator x in G, then the order of \gamma_3(G') is
finite and $n$-bounded. Here \gamma_3(G') is the third term of the lower
central series of G'.
