An ever-present limitation of transmission electron microscopy is the damage caused by high-energy electrons interacting with any sample. By reconsidering the fundamentals of imaging, we demonstrate an event-responsive approach to electron microscopy that delivers more information about the sample for a given beam current. Measuring the time to achieve an electron count threshold rather than waiting a predefined constant time improves the information obtained per electron. The microscope was made to respond to these events by blanking the beam, thus reducing the overall dose required. This approach automatically apportions dose to achieve a given signal-to-noise ratio in each pixel, eliminating excess dose that is associated with diminishing returns of information. We demonstrate the wide applicability of our approach to beam-sensitive materials by imaging biological tissue and zeolite.