Numerous experimental paradigms, such as forward suppression, critical-band measurements, and stimulus-specific adaptation, have revealed context-dependent computations at multiple stages of the auditory pathway.  Such context-dependent phenomena are more pronounced in the auditory cortex than at subcortical stages, suggesting cortical involvement in their generation.  What circuit mechanisms underly these flexible representations?  In order to disambiguate the contributions of synaptic depression, synaptic inhibition, and intrinsic adaptation, we manipulate the two main families of cortical interneurons – somatostatin-positive (Sst+) or parvalbumin-positive (Pvalb+) interneurons – while recording neural responses to tones or tone sequences in the auditory cortex of awake mice.  We show that cortical responses to a two-tone forward suppression paradigm in awake mice are more diverse than previously appreciated and vary with cell type.  We further show that inactivation of Sst+ interneurons increases response gain and reduces the bandwidth of forward suppression, while inactivation of Pvalb+ interneurons weakens tuning and decreases information transfer.  As an important caution, and contrary to the common assumption that tonic activation and inactivation are both manipulations that will produce valid, internally consistent insights into interneurons’ computational roles, we show that activating Sst+ and Pvalb+ interneurons reveals no such functional differences. We use a simple feedforward model to understand this asymmetry, and find that relatively small changes in key parameters, such as baseline activity, neural thresholds, or the strength of the light manipulation, determine whether activation and inactivation will produce equivalent conclusions regarding interneurons’ computational functions. This implies that seemingly minor experimental details can qualitatively change the readout of a neural population’s role in computation, and that the conclusions optogenetics enables us to draw regarding neuronal function can be influenced, even distorted, by the precise way in which the neuronal populations are manipulated.   Finally, we combine analysis of variability with a simple computational model to link the changes in forward suppression to changes in synaptic inhibition.