The dwell time ${\ensuremath{\tau}}_{D}$(E) and the transmission and reflection times ${\ensuremath{\tau}}_{T}$(E) and ${\ensuremath{\tau}}_{R}$(E), respectively, associated with the interaction of a particle of energy E with a one-dimensional barrier are currently the subject of considerable controversy. In this paper we prove that, despite a recent claim to the contrary, B\"uttiker's expression for the dwell time is correct. We use this fact in combination with a rigorous result derived by Hauge, Falck, and Fjeldly to prove that the phase times ${\ensuremath{\tau}}_{T}^{\ensuremath{\varphi}}$(E) and ${\ensuremath{\tau}}_{R}^{\ensuremath{\varphi}}$(E) cannot be identified with ${\ensuremath{\tau}}_{T}$(E) and ${\ensuremath{\tau}}_{R}$(E).