The use of control-theoretic solutions to detect attacks against cyber-physical systems is a growing area of research. Traditional literature proposes the use of control strategies to retain, f.i., satisfactory closed-loop performance, as well as safety properties, when a communication network connects the distributed components of a physical system (e.g., sensors, actuators, and controllers). However, the adaptation of these strategies to handle security incidents, is an ongoing challenge. In this paper, we analyze the use of a watermark-based detector that handles integrity attacks. We show that (1) the detector is able to work properly under the presence of adversaries using non-parametric methods to escape detection; but (2) it fails at detecting adversaries using parametric identification methods to escape detection. We propose a new strategy that complements the watermark-based detector in order to detect both adversaries. We validate the detection efficiency of the new strategy via numeric simulations