Extraclassical receptive field phenomena in V1 are commonly attributed to long-range lateral connections and/or extrastriate feedback. We address 2 such phenomena: surround suppression and receptive field expansion at low contrast. We present rigorous computational support for the hypothesis that the phenomena largely result from local short-range (< 0.5 mm) cortical connections and lateral geniculate nucleus input. The neural mechanisms of surround suppression in our simulations operate via (A) enhancement of inhibition, (B) reduction of excitation, or (C) action of both simultaneously. Mechanisms (B) and (C) are substantially more prevalent than (A). We observe, on average, a growth in the spatial summation extent of excitatory and inhibitory synaptic inputs for low-contrast stimuli. However, we find this is neither sufficient nor necessary to explain receptive field expansion at low contrast, which usually involves additional changes in the relative gain of these inputs.