Economy-wide rebound effects may undermine climate policies relying on energy efficiency improvements. However, available rebound estimates diverge widely. We illustrate the crucial role of model assumptions of household heterogeneity and elasticities. A computable general equilibrium model of the Austrian economy incorporates multiple household groups with heterogeneous preferences and analyzes how improving efficiency by 10% affects household fossil fuel consumption. In the base model, economy-wide rebound is 65%; different household groups show direct rebound of 8-12%; thus, economy-wide rebound is mainly advanced by indirect rebound. A sensitivity analysis using Monte Carlo simulation varies elasticities between household groups, namely substitutability between material and energy goods, and between different energy goods. In 160 simulation runs, the economy-wide rebound emerges as rather robust. By contrast, direct rebound varies widely among household groups and attains 30%, where reciprocal feedback between groups builds up. In the base model, a fossil fuel tax rate of 43% neutralizes the economy-wide rebound. When elasticities in 180 simulation runs are varied, this tax rate spans from 15% to 80%. Thus, rebound estimates and derived policy advice, such as specific rates and numbers, should be treated with great caution, unless elasticity parameters are reliable and account for heterogeneous consumer preferences.