Bob Dylan is a great singer.

Yes, in these post-“Idol” days, where even the most casual listener will point out someone’s “pitchiness,” the drive toward vocal perfection is a powerful one, a pursuit that Dylan does not share. His skill has always been in connection, in expression, in using his voice to capture the essence of the song he is singing.

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And with “Fallen Angels” (Columbia) — the companion to last year’s “Shadows in the Night,” where he also used Frank Sinatra’s versions of classics from the Great American Songbook as inspiration for interpretations of his own — Dylan shows how his connection to these songs and to his fans has only grown stronger, even as he is set to turn 75 next week.

Dylan infuses most of the songs here with a distinctively craggy beauty, instilling classics like “All the Way” and “It Had to Be You” with both swagger and lament, which makes the title “Fallen Angels” all the more fitting.

He is at his best on ballads like “Maybe You’ll Be There,” his world-weary vocals tinged with wistfulness and surrounded by a gorgeous, streamlined arrangement featuring Charlie Sexton and Stu Kimball’s understated guitar work. The importance of Dylan’s band — Sexton, Kimball, pedal-steel guitarist Donny Herron, bassist Tony Garnier and drummer George Receli — can’t be overstated, and the same goes for Dylan’s skills as an arranger. They set an elegant mood in “Polka Dots and Moonbeams” before Dylan even makes a sound, then support him as he stretches to charmingly reach higher notes.

The only time Dylan can’t quite match the band or the song is in “That Old Black Magic,” where the quickening tempo has him rushing to keep up.

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That slight misstep is so noticeable because everything else on “Fallen Angels” is so well-crafted, the impressive work of a great singer.