In this paper we consider a two-country model. Each country is characterised by several different sources of nominal inertia. This distinguishes our model from others in the so called New Open Economy Macroeconomics and makes it a suitable framework within which analyse the stabilising properties of monetary policies. We show that the variance of inflation induced by domestic inflationary shocks is lower under CPI targeting than when we target a measure of output price inflation. In fact, market segmentation and staggered wage and price setting result in lower and more persistent foreign inflation responses to a domestic inflationary shocks. This inertia in foreign price adjustments is completely passed through into CPI inflation but not into output price inflation. These differences cannot be detected in traditional models that usually introduce sluggish adjustments of domestic output prices as the only source of inertia. Furthermore, we find a limited role for the exchange rate in affecting the stabilising properties of the rules.