Neurons in primary visual cortex (area V1) are jointly tuned to the orientation and spatial frequency of sinusoidal stimuli (the Fourier domain). The role that suppressive mechanisms play in shaping the tuning and dynamics of cortical responses remains the subject of debate. Here we used subspace reverse correlation to study the relationship between suppression by non-optimal stimuli, the spectral-temporal separability of the responses, and their persistence in time. Two clear relationships emerged from our data: cells with inseparable responses were often accompanied by suppression to non-preferred stimuli, while separable responses showed mostly enhancement by their preferred stimuli. Additionally, inseparable responses were characterized by a longer persistence in time com-pared to those with separable dynamics. A parametric model that assumes the additive combination of separable enhancement and suppression signals, with suppression con-strained to be low-pass in spatial frequency and untuned for orientation, explained the data well. These new findings, in addition to an established correlation between selectivity and suppression for non-optimal stimuli, clarify how the dynamics and selectivity of cortical responses are shaped by suppressive signals and how their interplay generates the large diversity of responses observed in primary visual cortex.