This paper deals with feedback control of serial processes, that is, processes formed by the series connection of several subsystems. We focus on the determination of conditions under which a full multivariate controller may lead to performance improvements over a triangular controller. In other words, we study conditions under which it is advisable to include a control law with downstream feedback besides local control and feedforward action. The problem is addressed using an ℋ2 optimal performance criterion in a discrete-time framework. Our main result is a simple condition on the unstable poles, non minimum phase (NMP) zeros and delays of the discrete time plant model that ensures no penalization on the achievable performance under triangular control. As an application of this result, we show that for an application relevant class of serial processes, the condition can be expressed in terms of the time delays in each subsystem only. The derived condition may be useful for both process design and process control.