Using a standard New Keynesian model, we show that moderate side effects of zero lower bound (ZLB) policy suffice for positive lower bound (PLB) policy to pay off in terms of welfare, especially when central banks fail to commit. For given side effects of the ZLB, as the shock that makes the ZLB bind becomes larger and more persistent, the dominance of PLB policy over ZLB policy becomes more likely. The findings hold for flexible and rigid economies with both fast and slow potential output growth and low and high inflation targets.