Genetic circuits perform computational operations based on interactions between freely diffusing molecules within a cell. When transcription factors are combined to build a circuit, unintended interactions can disrupt its function. Here, we apply 'part mining' to build a library of 73 TetR-family repressors gleaned from prokaryotic genomes. The operators of a subset were determined using an in vitro method, and this information was used to build synthetic promoters. The promoters and repressors were screened for cross-reactions. Of these, 16 were identified that both strongly repress their cognate promoter (5- to 207-fold) and exhibit minimal interactions with other promoters. Each repressor-promoter pair was converted to a NOT gate and characterized. Used as a set of 16 NOT/NOR gates, there are >10⁵⁴ circuits that could be built by changing the pattern of input and output promoters. This represents a large set of compatible gates that can be used to construct user-defined circuits.