Rational engineering of biological systems is often complicated by the complex but unwanted interactions between cellular components at multiple levels. Here we address this issue at the level of prokaryotic transcription by insulating minimal promoters and operators to prevent their interaction and enable the biophysical modeling of synthetic transcription without free parameters. This approach allows genetic circuit design with extraordinary precision and diversity, and consequently simplifies the design-build-test-learn cycle of circuit engineering to a mix-and-match workflow. As a demonstration, combinatorial promoters encoding NOT-gate functions were designed from scratch with mean errors of <1.5-fold and a success rate of >96% using our insulated transcription elements. Furthermore, four-node transcriptional networks with incoherent feed-forward loops that execute stripe-forming functions were obtained without any trial-and-error work. This insulation-based engineering strategy improves the resolution of genetic circuit technology and provides a simple approach for designing genetic circuits for systems and synthetic biology.Unwanted interactions between cellular components can complicate rational engineering of biological systems. Here the authors design insulated minimal promoters and operators that enable biophysical modeling of bacterial transcription without free parameters for precise circuit design.