A key property of neurons in primary visual cortex (V1) is the distinction between simple and complex cells. Recent reports in cat visual cortex indicate the categorization of simple and complex can change depending on stimulus conditions. We investigated the stability of the simple/complex classification with changes in drive produced by either contrast or modulation by the extraclassical receptive field (eCRF). These two conditions were reported to increase the proportion of simple cells in cat cortex. The ratio of the modulation depth of the response (F1) to the elevation of response (F0) to a drifting grating (F1/F0 ratio) was used as the measure of simple/complex. The majority of V1 complex cells remained classified as complex with decreasing contrast. Near contrast threshold, an equal proportion of simple and complex cells changed their classification. The F1/F0 ratio was stable between optimal and large stimulus areas even for those neurons that showed strong eCRF suppression. There was no discernible overall effect of surrounding spatial context on the F1/F0 ratio. Simple/complex cell classification is relatively stable across a range of stimulus drives, produced by either contrast or eCRF suppression.