  Proving achievability of protocols in quantum Shannon theory usually does not
consider the efficiency at which the goal of the protocol can be achieved.
Nevertheless it is known that protocols such as coherent state merging are
efficiently achievable at optimal rate. We aim to investigate this fact further
in a general one-shot setting, by considering certain classes of decoupling
theorems and give exact rates for these classes. Moreover we compare results of
general decoupling theorems using Haar distributed unitaries with those using
smaller sets of operators, in particular $\epsilon$-approximate 2-designs. We
also observe the behavior of our rates in special cases such as $\epsilon$
approaching zero and the asymptotic limit.
