  Suppose that some harmonic analysis arguments have been invoked to show that
the indicator function of a set of residue classes modulo some integer has a
large Fourier coefficient. To get information about the structure of the set of
residue classes, we then need a certain type of complementary result. A
solution to this problem was given by Gregory Freiman in 1961, when he proved a
lemma which relates the value of an exponential sum with the distribution of
summands in semi-circles of the unit circle in the complex plane. Since then,
Freiman's Lemma has been extended by several authors. Rather than residue
classes, one has considered the situation for finitely many arbitrary points on
the unit circle. So far, Lev is the only author who has taken into
consideration that the summands may be bounded away from each other, as is the
case with residue classes. In this paper we extend Lev's result by lifting a
recent result of ours to the case of the points being bounded away from each
other.
