We provide new evidence on the relationship between inflation and its uncertainty in the United States on an historical basis, covering the period from 1775 to 2014. First, we use a bounded approach for measuring inflation uncertainty, as proposed by Chan et al. (2013), and compare the results with the Stock and Watson (2007) and Chan (2015) methods. Second, we employ the wavelet methodology to analyze the comovements and causal effects between the two series. Our results provide evidence of a relationship between inflation and its uncertainty that varies across time and frequency. First, we show that in the medium and long runs, the Freidman–Ball hypothesis holds with a bounded measure of uncertainty, while if the Stock and Watson (2007) measure of uncertainty is used, the Cukierman–Meltzer reasoning prevails. Therefore, the findings are sensitive to the way inflation uncertainty is computed. Second, we discover mixed evidence about the inflation–uncertainty nexus in the short run, findings that explain the mixed results reported to date in the empirical literature.