Changing the structure of the economy is often considered an option to reduce environmental impacts – for example, by changing the mix of sectors in the economy, the energy mix of production, or the mix of origin countries for imported products. To study the effect of such structure (or mix) effects, researchers often use index decomposition analysis (IDA). This study uses experimental data to show that most existing IDA methods, especially the widely used LMDI (logarithmic mean divisia index), yield results that are difficult to understand and easily misinterpreted. We use formal proof to demonstrate that: The LMDI interpretation problem is due to the use of shares to describe the considered mix. We developed an alternative method, the Marshall-Edgeworth with Structure Effects (MESE). The MESE defines structure effects by comparing each observation to a hypothetical average, which better reflects the common understanding of structure effects. We compared empirical data on the LMDI and the MESE, analysing the effect of the changing sector mix on energy use in the USA from 1995 to 2016, and found that results from the two tools differed significantly. We therefore recommend using the MESE when structure effects are included in IDA.