Contrast sensitivity is known to be strongly influenced by the target surround, yet the role of the surround interaction in visual processing remains unclear. Previously, we have shown that the surround strongly suppresses contrast sensitivity in the periphery when the surround spatial frequency and orientation match those of the target (Petrov, Carandini, & McKee, 2005). Here, we explore how various spatial characteristics of the iso-oriented and frequency-matched surround, such as surround phase and spatial layout, affect suppression. We manipulated surround geometry (annulus ring, half annulus, and bow tie) and its separation from the target (both laterally and in depth) and varied the position of the half-annulus and bow-tie surrounds with respect to Gabor target's orientation and with respect to its location in the visual field (i.e., radial vs. tangential surrounds). We also compared monoptic, dichoptic, and binocular surround suppression. Except for a significant radial-tangential anisotropy, only the area of the surround and the lateral separation between the surround and target had a significant effect on the magnitude of suppression. We showed that, although suppression amplitude remains constant with stimulus eccentricity, the lateral extent of suppression scales in proportion to the eccentricity. The most surprising finding was that the extent of surround suppression does not scale with stimulus size or spatial frequency. We suggest that the properties of surround suppression are best explained by a mechanism that selects salient targets for subsequent saccades.