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The present study investigates the influence of attention modulation on neural tuning functions under a Gaussian correlation structure. Recent experiments have shown that attention modulates the tuning curve via its height and base rate. Inspired by this experimental finding, we previously showed the effective size of attention modulation (i.e. the critical length) on the neural population that enhances encoding accuracy. The previous result, however, was obtained under the assumption of uncorrelated firing, i.e. stimulus-conditional independence of neural responses. A question still remains whether the above findings can be applied to correlated firing. It is important to investigate this issue partly because neural firings are usually correlated but even more so because common attentional inputs may cause correlated firings. The present study first provides the general framework of attention modulation in relation to an attended stimulus and an actual stimulus and then shows the existence of a critical length under a Gaussian correlation structure. In order to improve encoding accuracy, measured by the Fisher information, the height and the base rate should be increased when the attended stimulus is in the critical length from the peak of the tuning curve and decreased otherwise. Furthermore, we confirm that a similar nature of the critical length also holds even when the neural decoder uses an uncorrelated unfaithful model. Thus, the existence of the critical length seems to be a ubiquitous phenomenon in attention modulation, and so its implications are discussed. [Copyright &y& Elsevier]