The strong and sustained rise in oil prices observed in recent years poses a challenge to monetary policy and its ability to simultaneously achieve low inflation and stable output. Against this background, the paper studies monetary policy in a small open economy New Keynesian DSGE model including oil as a production input and a component of final demand. It investigates the performance of alternative price level definitions, notably headline and core CPI, in standard interest rate rules with respect to output and inflation stabilisation. The analysis puts special emphasis on the impact of price and real wage rigidity and their interaction on the policy trade-off induced by the oil price shock. While the degree of price rigidity alone is found to have little impact on the shock transmission and generates only small differences between alternative monetary strategies, the simulations suggest a more important role for real wage stickiness. Real wage stickiness triggers second round effects and complicates stabilisation whatever the policy rule. A focus on core inflation tends to limit the contraction of output in this context. The results also point to some interaction between nominal price and real wage rigidities. In the presence of real wage rigidity, greater price flexibility is found to be destabilising, as it amplifies the initial inflation effect of shocks, thereby triggering a stronger monetary policy response and a larger output effect.