We quantify the impact of the European Emission Trading Scheme (ETS) on the two dimensions of competitiveness - production and profitability - for the iron and steel industry. Among those covered by the scheme, this sector is one of the most exposed, since it is both highly CO2-intensive and relatively open to international trade. We also examine the robustness of these results to various assumptions: marginal abatement cost curve, trade and demand elasticities, as well as pass-through rates and updating of allocation rules, of which the latter two are scarcely debated. We conclude that for this sector, competitiveness losses are small. We prove this conclusion to be robust. Hence arguments against tightening the environmental stringency of the ETS in Phase II are not justified on grounds of competitiveness loss. Our systematic sensitivity analysis allows us to identify the important assumptions for each output variable. It turns out that pass-through rates and updating rules are significant, despite being often implicit and least debated in existing analyses.