One fundamental problem of neuronal information processing is posed by the enormous divergence and convergence of synaptic connections in and between many brain structures. This suggests that neurons receive not only signals which are relevant for their present computational task, but are often exposed to a large amount of unrelated, arbitrary signals which disturb ongoing information processing. This is particularly evident in vision when viewing natural, densely cluttered scenes. Neurons in higher visual areas with large receptive fields receive signals caused by a variety of different stimuli at the same time. Nevertheless they are capable of restricting their processing largely to the attended stimulus (Reynolds, Chelazzi, & Desimone, 1999). Thus, selective processing of the behaviorally relevant stimulus often occurs while large parts of a neuron’s synaptic input is expected to carry signals which reflect arbitrarily different stimuli. These unrelated signals can not be considered to behave like stationary and independent noise signals which might be discarded by simple subtraction. They are caused by real stimuli, and therefore they appear and disappear, increase and shrink, correlate and de-correlate in the same non-stationary manner as the signals for the relevant stimulus. Given the evidence for spatio-temporal structure in ongoing activity (Arieli, Sterkin, Grinvald, & Aertsen, 1996), even synaptic inputs carrying no stimulus information do not conform to typical assumptions of stationarity and independence. Since the relevant stimulus may cover only a small part of the classical receptive field, the number of irrelevant signals may easily outnumber the relevant signals by an order of magnitude and more. Therefore attention and other cognitive processes require a mechanism capable of reducing strongly and selectively the influence of large parts of the synaptic input to a neuron and to increase the effectiveness for a potentially small part carrying the computationally relevant signals. Modeling studies have suggested different solutions to control signal routing. Models based on gating neurons