Intrinsic signal optical imaging reveals a highly modular map of orientation preference in the primary visual cortex (V1) of several species. This orientation map is characterized by domains and pinwheels where local circuitry is either more or less orientation selective, respectively. It has now been repeatedly demonstrated that neurons in pinwheels tend to be more broadly tuned to orientation, likely due to the broad range of orientation preference of the neighboring neurons forming pinwheels. However, certain stimulus conditions, such as a decrease in contrast or an increase in size, significantly sharpen tuning widths of V1 neurons. Here, we find that pinwheel neuron tuning widths are broader than domain neurons only for high contrast, optimally sized stimuli, conditions that maximize excitation through feedforward, and local cortical processing. When contrast was lowered or size increased, orientation tuning width sharpened and became equal. These latter conditions are conducive to less local excitation either through lower feedforward drive or by surround suppression arising from long-range cortical circuits. Tuning width differences between pinwheel and domain neurons likely arise through more local circuitry and are overcome through recruitment of longer-range cortical circuits.