I compare nominal gross domestic product (GDP) level targeting with strict price level targeting in a small New Keynesian model, with the central bank operating under optimal discretion and facing a zero lower bound on nominal interest rates. I show that, if the economy is only buffeted by purely temporary shocks to inflation, nominal GDP level targeting may be preferable because it requires the burden of the shocks to be shared by prices and output. However, in the presence of persistent supply and demand shocks, strict price level targeting may be superior because it induces greater policy inertia and improves the tradeoffs faced by the central bank. During lower bound episodes, somewhat paradoxically, nominal GDP level targeting leads to larger falls in nominal GDP.