In this paper we provide new empirical evidence relevant for discussions on monetary policy independence in the context of euro adoption in three Central and Eastern European (CEE) countries: Czechia, Hungary and Poland. Unlike many other authors, in this paper we focus on real and not nominal interest rates as real interest rates are at the hearth of modern macroeconomic and monetary policy theory. In the paper we employ several methodologies to test the convergence of real interest rates between these countries and the euro area and to determine the main drivers of real interest rates. Based on the unit root analysis we find evidence of convergence of real interest rates in these countries, thus confirming the real interest rate parity (RIRP) hypothesis. Next, using principle component analysis (PCA) we show that common factor extracted from the sample of CEE countries and individual euro area countries can explain high proportion of real interest rate developments in these countries. Finally, results of our newly proposed analytical framework for the analysis of determinants of real interest rates in small open economies, based on a Bayesian VAR model with block exogeneity, show that external shocks have non-negligible effect on real interest rate developments in selected CEE countries. Thus, our results indicate that real interest rates in CEE depend on factors that are beyond the scope of domestic monetary policy makers. In this sense we can conclude that (conventional) monetary policy independence in these countries is limited. Thus, we see the loss of monetary policy independence as overly emphasized argument in discussions on the euro adoption in these countries. However, we are aware that national central banks in CEE started to rely more on non-conventional measures recently, which gives them a higher degree of flexibility (and autonomy).