Aiming at both low prices and innovation, policy makers and economists have long argued about the optimal intensity of competition. While the current discussion in telecommunication regulation points out that competition can be detrimental to innovation due to the low appropriability of rents established economic approaches advocate competition to be conducive to innovation. This reflects the dispute in economics between Schumpeterian and neoclassical theories. Aghion et al. (2005) offered reconciliation by modelling an inverted U relationship, which this paper tests for European mobile phone providers. Innovation is measured by a service launch indicator and R&D investments, and competition is approximated by market concentration. As markets are clearly defined, problems of market definition which usually blur concentration indices are avoided. The paper finds robust and statistically significant support for the tested quadratic relationship for both innovation indicators. The innovation optimising Herfindahl-Hirschman was at around 5,500 between 2001 and 2003, but may vary over time. This finding points at a conflict in the realisation of the regulatory objectives of low prices and innovation at the same time.