  Transfer Krull monoids are a recent concept including all commutative Krull
domains and also, for example, wide classes of non-commutative Dedekind
domains. We show that transfer Krull monoids are fully elastic (i.e., every
rational number between $1$ and the elasticity of the monoid can be realized as
the elasticity of an element). In commutative Krull monoids which have
sufficiently many prime divisors in all classes of their class group, the set
of catenary degrees and the set of tame degrees are intervals. Without the
assumption on the distribution of prime divisors, arbitrary finite sets can be
realized as sets of catenary degrees and as sets of tame degrees.
