Stand-up comic Bill Burr had a more dramatic role in AMC’s “Breaking Bad.” (Koury Angelo)

Bill Burr doesn’t want to lose his edge, so he tries not to think too hard about his thriving career. Still, he acknowledges that headlining Constitution Hall is a big deal. After all, it’s the venue where Eddie Murphy filmed his landmark 1983 special “Delirious.” “It’s definitely a milestone,” says Burr, 45, who’s gaining steam thanks to supporting roles in “Breaking Bad” and “The Heat.”

Rolling Stone just wrote a story calling you “The New Louis C.K.” How did you react to that?
I owe Louis an apology. That guy’s put out 10 times the amount of specials I have — all I do is put out a special every two years. I guess because we’re both balding redheads [we’re the same]. That took the wind out of my sails a little bit.

Can you tease your new material?
I’m not trashing women at all this time, [like in] the final 25 minutes of my last special. I decided to grow up and figured out [those] issues were on me. I’m sort of examining my own issues.

When I saw you at the DC Improv last year, you seemed to enjoy riffing on the government. What did you make of the shutdown?
You really have this parental relationship with your government and country and I was amazed at how much of the government could shut down. Yeah, you can’t go to the Lincoln Memorial but I could still go out and get a sandwich. I thought it was going to affect me more.

You had a memorable role as Kuby, one of Saul Goodman’s (Bob Odenkirk) thugs on “Breaking Bad.” Did you like the ending?
I loved it. I thought it was just a perfect series. The only bad feeling I have just as a fan is that it’s over. I owe [creator] Vince Gilligan my acting career. I still can’t believe I got to be a very small part of it. Because of the scenes I got to do, I was able to break out of the idea that because you’re a comedian you can’t do drama.

Has there been talk of you being in AMC’s “Better Call Saul” spinoff series? Would you want to do it?
I haven’t heard anything. Oh my god, are you kidding me? To work for a genius at Vince’s level again? If he was doing a rip-off of “Glee” I would do it. I’d be taking singing and dancing lessons.

DAR Constitution Hall, 1776 D St. NW; Thu., 7:30 p.m., $47; 202-628-4780. (Farragut West)