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Improvements in energy efficiency reduce the cost of consuming services from household cars and appliances and can result in a positive rebound effect that offsets part of the direct energy savings. We use a general equilibrium model to derive analytical expressions that allow us to compare rebound effects from a costless technology shock (CTS) to those from a costly energy efficiency standard (EES). We decompose each total effect on the use of energy into a direct efficiency effect, direct rebound effect, and indirect rebound effect. We show which factors determine the sign and magnitude of each. Rebound from a CTS is generally positive, as in prior literature, but we also show how a pre-existing EES can negate the direct energy savings from the CTS – leaving only the positive rebound effect on energy use. Then we analyze increased stringency of an EES, and we show exactly when the increased costs reverse the sign of rebound. Using plausible parameter values in this model, we find that indirect effects can outweigh the direct effects captured in partial equilibrium models, and that the total rebound from a costly EES can be negative.