In this paper we consider the application of importance sampling in simulations of Markovian tandem networks in order to estimate the probability of rare events, such as network population overflow. We propose a heuristic methodology to obtain a good approximation to the ?optimal? state-dependent change of measure (importance sampling distribution). Extensive experimental results on 2-node tandem networks are very encouraging, yielding asymptotically efficient estimates (with bounded relative error) where no other state-independent importance sampling techniques are known to be efficient. The methodology avoids the costly optimization involved in other recently proposed approaches to approximate the ?optimal? statedependent change of measure. Moreover, the insight drawn from the heuristic promises its applicability to larger networks and more general topologies.