Clean energy technologies, such as photovoltaics, wind turbines, efficient lighting systems and electric vehicles, are key players in moving towards a sustainable future. However, each of these technologies relies on significant use of specialized metals, raising materials criticality concerns as the demand for these devices (and the materials they contain) increases. In addition to low ore concentrations and missing trade at major public exchanges, one of the main sources of concern is their byproduct nature. In many cases, in fact, such metals are obtained as minor products of more abundant materials, which are referred as carrier metals. Some examples include cadmium, gallium, germanium, indium, selenium and tellurium. The point discussed within the current literature is that the maximum supply potential of byprod-uct metals is limited by the supply of carrier metals. Moreover, price inelasticity of byproducts (supply not responding to price changes) have been cited as proof of such constraint. The first part of the present work aims to categorize forty-seven carrier-byproduct pairs according to byproduct fraction and value ratio to assess criticality. Both a qualitative and a quantitative evaluation of the obtained matrix are performed, using hierarchical clustering for the quantitative analysis. The objective of the second part of the study is to verify whether the supply of byproduct metals is inelastic and, if so, understand whether this is caused by carriers’ supply limiting byproduct sup-ply. Indium and tellurium are used as case studies. The selection of those elements is driven by their wide application in clean energy technologies, from thin-film photovoltaics cells to nuclear power control rods. Econometric analyses including ordinary least squares, autoregressive distrib-uted lag and two stages least square models are performed. Five similar groups are identified in both the qualitative and quantitative evaluation. Each cluster consists of pairs with similar overall criticality that impact market players in a similar way. Two groups are found to be critical for consumers, one for producers, one for both and one for none. For what concerns supply inelasticity, econometric analyses suggest that both indium and tellu-rium are price inelastic to supply. However, while in the first case the reason is found to be limita-tion of the carrier metal, for tellurium this seems not to be the case. Non-transparent trading, monopolistic character of supply and other factors are indeed expected to be the major causes. Future work will investigate additional byproduct pairs using similar econometric models. The final aim of the project is to produce outcomes which will be useful for decision making of both metals producers and consumers.