  Understanding the dynamics of higher-dimensional quantum systems embedded in
a complex environment remains a significant theoretical challenge. While
several approaches yielding numerically converged solutions exist, these are
computationally expensive and often provide only limited physical insight. Here
we address the question when more intuitive and simpler to compute
weak-coupling approaches still provide adequate accuracy. We develop a simple
analytical criterion and verify its validity for the case of the much-studied
FMO dynamics as well as the canonical spin-boson model.
