Trampled by Turtles return to an international broadcast stage tonight on "Late Show With David Letterman." / Photo by Stephan Hoglund for Star Tribune

Trampled by Turtles and Poliça owe Tom Waits a great big thank-you, besides the obvious gratitude every rock musician who doesn't sing fluff owes the howling Rock and Roll Hall of Famer. The two ascending Minnesota bands each picked up the national TV spots that Waits postponed this week, for reasons not explained.

TBT will be filling in for him tonight on "The Late Show With David Letterman," appearing after Amy Poehler. The Trampled guys just performed in Manhattan exactly one week ago at Webster Hall. A representative from the Letterman show did indeed attend the gig with an eye for booking them in the future, according to the band's publicist, but then lo and behold the date opened up for them right away. Perhaps "The Late Show's" Thunder Bay-reared bandleader Paul Shaffer is also hip to the Duluth pickers since they're roughly from his neck of the woods. TBT had to postpone a date tonight in Carrboro, N.C., to pick up their national-TV debut. Here's betting Letterman makes a quip about their band name, just like Garrison Keillor did. The show airs on CBS locally starting at 10:35 p.m.

Poliça earned Waits' second postponed TV spot Wednesday on "Late Night With Jimmy Fallon," which promises to be an especially high-profile night and week to be on the NBC show. It comes one night after President Barack Obama's much-ballyhooed appearance opposite Fallon. On Wednesday, the lead guest before Channy and the boys will be the cast of "30 Rock," which is gearing up for another live episode of their show on Thursday. Fallon's staff might have grown hip to Poliça through its affiliation, er, affiliyation with Gayngs, which performed on the show in 2010. NBC airs "Late Night" locally starting at 11:35 p.m.

We likely won't see either of these bands performing back in the Twin Cites until June, when TBT plays Rock the Garden outside Walker Art Center (June 16) and Polica helps inaugurate the River's Edge Festival on Harriet Island (June 23). The Trampled crew will squeeze in one Duluth gig during a short tour respite on May 2 at Clyde Iron Works, part of the Homegrown Festival.

Here's the new video for the song that TBT will probably perform on air tonight.