Standard small-scale New Keynesian models (NKM) come with considerable output losses from moderate positive steady-state inflation when the long-run output-inflation relationship is derived from the microeconomic equations. We analyse 1. which trend-inflation-dependent parameter change might move the New Keynesian model’s long-run Phillips curve (LRPC) towards superneutrality and hence bring about a more moderate output impact of steady-state inflation and 2. whether this same parameter change also turns the linearised short-run New Keynesian Phillips curve (NKPC) into the empirically found direction across different trend inflation rates.The parameter change across trend inflation rates should be at least tentatively empirically justified. Two parameters meet our criteria: the usual suspect, the Calvo-parameter, and the intertemporal elasticity of substitution. Last but not least, allowing these parameters to change across trend inflation rates produces impulse responses more in line with “stylised facts” than those of a constant parameter trend inflation model. We consider the impact of each trend-inflation-dependent parameter separately but also a combination of the two.