This paper discusses the likely evolution of U.S. inflation in the near and medium term on the basis of (1) past U.S. experience with very low levels of inflation, (2) the most recent Japanese experience with deflation, and (3) recent U.S. micro evidence on downward nominal wage rigidity. Our findings question the view that stable long-run inflation expectations and downward nominal wage rigidity will provide sufficient support to prices such that deflation can be avoided. We show that an inflation model fitted on Japanese data over the past 20 years, which accounts for both short- and long-run inflation expectations, matches the recent U.S. inflation experience quite well. While the model indicates that U.S. inflation might be subject to a lower bound, it does not rule out a prolonged period of mild deflation going forward. In addition, our micro evidence on wages suggests no obvious downward rigidity in the firm's wage costs, downward rigidity in individual wages notwithstanding. As a consequence, downward nominal wage rigidity may provide little offset to deflationary pressures in the current U.S. situation, despite some circumstantial evidence that this channel might have been at work in the past.