Band-spectrum noise has been shown to suppress the visual perception of printed letters. The suppression exhibits a specific dependence on the spatial frequency of the noise, and the frequency domain of most effective inhibition has been related to the size of the letters. In this paper, we address two important questions that were left open by previous studies: (1) Is the observed effect specific to text, and which parameters determine the domain of most effective suppression? (2) What is the origin of the effect in terms of underlying neural processes? We conduct a series of psychophysical experiments that demonstrate that the frequency domain of most effective inhibition depends on the stroke width of the letter rather than on the letter size. These experiments also demonstrate that the effect is not specific to the recognition of letters but also applies to other objects and even to single bars. We attribute the observed effect to nonclassical receptive field (non-CRF) inhibition in visual area V1. This mechanism has previously been suggested as the possible origin of various other perceptual effects. We introduce computational models of two types of cell that incorporate non-CRF inhibition, which are based on Gabor energy filters extended by surround suppression of two kinds: isotropic and anisotropic. The computational models confirm previous qualitative explanations of perceptual effects, such as orientation contrast pop-out, reduced saliency of lines embedded in gratings, and reduced saliency of contours surrounded by textures. We apply the computational models to the images used in the psychophysical experiments. The computational results show a dependence of the inhibition effect on the spatial frequency of the noise that is similar to the suppression effect measured in the psychophysical experiments. The experimental results and their explanation give further support to the idea of a possible functional role of non-CRF inhibition in the separation of contour from texture information and the mediation of object contours to higher cortical areas.