The most common New-Keynesian model--with sticky-prices--has potentially implausible implications in a zero-lower bound environment. Fiscal and forward guidance multipliers can be implausibly large. Moreover, the sticky-price model implies that positive supply shocks, such as an increase in productivity, will lower production, and that increased price flexibility can exacerbate such a decline in output (as well as amplifying the effects of other shocks). These results are fragile and disappear under a plausible alternative to sticky prices--sticky information: Fiscal and monetary multipliers are smaller, positive supply shocks raise output, and greater price flexibility, in the sense of more frequent updating of information, moves the economy's response toward the neoclassical benchmark. These results suggest caution in drawing policy lessons from a single, sticky-price framework. Finally, we highlight how strategies akin to nominal-income targeting can enhance the ability of policymakers to affect demand in sticky-price and sticky-information models.