  We study the notion of positive and negative complexity of pairs of objects
in cluster categories. The first main result shows that the maximal complexity
occurring is either one, two or infinite, depending on the representation type
of the underlying hereditary algebra. In the the second result, we study the
bounded derived category of a cluster tilted algebra, and show that the maximal
complexity occurring is either zero or one whenever the algebra is of finite or
tame type.
