They're one of the buzziest buzz bands of 2012, and they're out on the road promoting their Top 20 debut full-length LP, so you know what that means -- it's time for the Alabama Shakes to start making the late-night talk show circuit before the inevitable backlash begins in earnest.

The band stopped by 'The Late Show with David Letterman' last night (April 12), just in time to help celebrate Dave's birthday with a performance of 'Hold On,' the leadoff track from their just-released new record, 'Boys & Girls.' Though Dave didn't get to present the Shakes' late-night debut -- that honor went to Conan O'Brien, who hosted them in February -- last night's appearance found the band in fine form, tearing through 'Hold On' with enough vim and vigor to easily demonstrate why they're generally regarded as one of the year's most exciting debut acts.

Letterman seemed to agree, telling the band their performance was "lovely" -- and if you know Letterman, you know he doesn't part with compliments lightly. Take a look at the clip embedded below and let us know what you think. Have you listened to 'Boys & Girls' yet? And if you haven't, is this enough to convince you to make the purchase?

Watch Alabama Shakes Perform 'Hold On'