A seal device having a substantially conical shape including a slit opening at its tip defined by a pair of planar surfaces, the opening reinforced by gussets on the exterior surface of the seal device and adjacent to the end regions of the slit. The gussets help bias the ends of the slit towards a closed position, even when an instrument is located within the slit, to thereby reduce “cat-eye”-ing and minimize leakage therethrough. The seal device may include ramps on respective inner surfaces of the device, the ramps functioning as a lead-in to the slitted opening such an inserted instrument contacts the ramps first and opens the slit prior to the instrument contacting the material of the slit. Along the outer surface of the device is a flexible body portion to minimize the effect on the opening when an instrument is inserted into the device.
