A plethora of security schemes for wireless sensor networks (WSNs) has been proposed and their resilience to various attacks analyzed; including situations the adversary compromises a subset of the WSN nodes and/or deploys own misbehaving devices. The higher the degree of such intrusion is, the more effective an attack will be. Consider, however, an adversary that is far from omnipotent: How should she attack, how should she deploy her resources to maximally affect the attacked WSN operation? This basic question has received little attention, with one approach considering genetic algorithms for devising an attack strategy . In this work, we recast the problem towards a more systematic treatment and more computationally efficient solutions: a combination of a genetic algorithm with a convex relaxation, and an ℓ1- constraint formulation. The devising of near-optimal attack strategies efficiently strengthens the adversary, allowing her to adapt and mount effective and thus harmful attacks even in complex and dynamically changing settings.