  We study the dynamics and trapping of excitations for a dimer with an energy
off-set $\Delta$ coupled to an external environment. Using a Lindblad quantum
master equation approach, we calculate the survival probability $\Pi(t)$ of the
excitation and define different lifetimes $\tau_s$ of the excitation,
corresponding to the duration of the decay of $\Pi(t)$ in between two
predefined values. We show that it is not possible to always enhance the
overall decay to the trap. However, it is possible, even for not too small
environmental couplings and for values of $\Delta$ of the order ${\cal O}(1)$,
to decrease certain lifetimes $\tau_s$, leading to faster decay of $\Pi(t)$ in
these time intervals: There is an optimal environmental coupling, leading to a
maximal decay for fixed $\Delta$.
