In this work we analyze, explore and measure two of the most important concepts for the theory of storable commodity markets. After analyzing the statistical properties of spot and futures EU ETS allowances for Germany and France, we model and test the risk premium and convenience yield for CO2 contracts accordingly to previous economic theories, for the period 2005-2009. Results indicate that convenience yields are positively related to the spot CO2 return while being negatively influenced by the spot volatility. This negative impact of spot volatility is also verified for the risk premium, with the latter varying positively with time to maturity. Contradicting previous empirical findings, we found only a positive influence of the convenience yield on the risk premium for the ECX French market and for Phase II contracts, leading us to conclude that results are Phase, market and data span dependent. Moreover, results are independent on the volatility forecast used and important for risk management purposes for allowances markets participants. Moreover, day-ahead markets for CO2 are in "normal contango" for the entire data period under analysis, contrary to previous empirical findings for the allowances market.