Simple cells in the primary visual cortex have segregated ON and OFF subregions in their receptive fields, while complex cells have overlapping ON and OFF subregions. These two cell types form the extremes at each end of a continuum of receptive field types. Hubel and Wiesel in 1962 suggested a hierarchical scheme of processing whereby spatially offset simple cells drive complex cells. Simple and complex cells are often classified by their responses to moving sine wave gratings: simple cells have oscillatory responses while complex cells produce unmodulated responses. Here, using moving gratings as stimuli, we show that a significant number of cells that display low levels of response modulation at high contrasts demonstrate high levels of response modulation at low contrasts. Most often a drifting low contrast grating generates a large phasic response at the fundamental frequency of the grating (F1) and a smaller but significant phasic response that is approximately 180 deg out-of-phase with the F1 component. We present several models capable of capturing the effects of stimulus contrast on complex cell responses. The model that best reproduces our experimental results is a variation of the classical hierarchical model. In our model several spatially offset simple cells provide input to a complex cell, with each simple cell exhibiting a different contrast response function. At low contrasts only one of these simple cells is sufficiently excited to reveal its receptive field properties. As contrast is increased additional spatially offset simple cells with higher contrast thresholds add their responses to the overall spiking activity.