Recently it has been argued that a monetary policy of nominal income targeting would result in dynamically unstable processes for output and inflation. That result holds in a theoretical model that includes backward-looking IS and Phillips curve relations, but these are rather special and theoretically unattractive. The present paper demonstrates that replacement of the special Phillips curve with one of several more plausible specifications overturns the instability result, whether or not the IS equation is replaced with a forward-looking version. Thus the instability result is quite fragile and therefore provides almost no basis for a negative judgment regarding nominal income targeting.