In this paper, we revisit the subject of country-level macroeconomic adjustment in the euro area in the absence of autonomous monetary and exchange rate policy. We discuss how the real interest rate mechanism and the competitiveness (real exchange rate) channel interact with various aspects of countries' heterogeneity. Our stylized New Keynesian model of a structurally heterogenous monetary union comprises country-specific empirical hybrid IS and Phillips curves and common Taylor rule. It extends the standard closed-economy specification and replicates both effects in question. Cross-country long-term differentials in steady-state inflation (due to structural factors, such as Balassa-Samuelson effect) and natural interest rate do not rule out the existence of an equilibrium, as long as they are offset by additional price level differentials. We establish a link between the smoothness of the adjustment process and various aspects of countries' heterogeneity, such as expectation formation mechanisms, inflation persistence, market flexibility, as well as output gap sensitivity to real interest rate, real exchange rate and foreign demand. Our GMM estimates of the IS and Phillips curves imply that the competitiveness channel is effectively at work in EMU 12 in the sense of real exchange rate influence on the output gap, but market flexibility necessary to trigger shifts in REER remains below the standards in New Keynesian empirical literature. They also suggest that the risk of the real interest rate effect is reduced by low output gap responsiveness to country-specific real interest rates, coupled with mostly significant responses to real exchange rates, and mainly results from intrinsic inflation persistence. Our model does not confirm the existence of a premium when foreign markets are more rigid in relative terms. Promoting market flexibility, combating intrinsic inflation persistence, anchoring inflation expectations and intensifying trade linkages remain the main challenges for policymakers willing to minimize the procyclical effects of real interest rate and maximize the efficiency of competitiveness channel as a substitute for autonomous monetary policy.