This work contrasts conservative or minimally mutilating revisions of empirical theories as they are identified in the presently dominant AGM model of formal belief revision and the structuralist program for the reconstruction of empirical theories. The aim is to make understandable why both approaches only partly succeed in substantially informing and formally restraining the issue. With respect to the rationality of minimal change, the overall result is negative. Readers with an interest in formal epistemology are provided with application cases (mercury anomaly, revision of early thermo-dynamics, introduction of the neutrino), the historically inclined reader is offered a systematic perspective. The discussion can largely be followed without a background in formal logic.