Transiently powered computers (TPCs) form the foundation of the battery-less Internet of Things, using energy harvesting and small capacitors to power their operation. This kind of power supply is characterized by extreme variations in supply voltage, as capacitors charge when harvesting energy and discharge when computing. We experimentally find that these variations cause marked fluctuations in clock speed and power consumption. Such a deceptively minor observation is overlooked in existing literature. Systems are thus designed and parameterized in overly conservative ways, missing on a number of optimizations.We rather demonstrate that it is possible to accurately model and concretely capitalize on these fluctuations. We derive an energy model as a function of supply voltage and prove its use in two settings. First, we develop EPIC, a compile-time energy analysis tool. We use it to substitute for the constant power assumption in existing analysis techniques, giving programmers accurate information on worst-case energy consumption of programs. When using EPIC with existing TPC system support, run-time energy efficiency drastically improves, eventually leading up to a 350% speedup in the time to complete a fixed workload. Further, when using EPIC with existing debugging tools, it avoids unnecessary program changes that hurt energy efficiency. Next, we extend the MSPsim emulator and explore its use in parameterizing a different TPC system support. The improvements in energy efficiency yield up to more than 1000% time speedup to complete a fixed workload.