But the country rock group, or at least its members, is anything but notorious. Not when folks like Rodney Crowell, Vince Gill, Tony Brown and a bunch of longstanding ace Nashville sidemen stalwarts are aboard.
In fact, the album may mark the debut music from the group, but this is not the first time most of them played together.
The Cherry Bombs - most of them - actually were the well-regarded backing band for Crowell about 25 years ago.
Crowell says during a cell phone interview somewhere on the road in New Mexico that his intent in making the record was "honestly, trying to have some fun. And trying not to take it too seriously. As a matter of fact, I wasn't even concerned with making the best album I can. I didn't care about that. To me, it was just Vince and I hadn't worked together in a long time. That was one of the things that I was interested in. Vince and I hadn't hooked up in years because we've been on two different paths."
Crowell says his time with Gill in their previous musical lives "was just a barrel of laughs. We just laughed all the time, having some fun and having some laughs."
And Crowell indicates they continued with that same attitude on the self-titled disc out in late July on the single with the ultra long title, "It's Hard to Kiss the Lips at Night That Chew Your Ass Out All Day Long."
The very funny song is a man talking about his woman, who used to treat him a helluva better, but he can't much stand her any more.
"She used to call me baby, I thought she was such a lady/But my how things have changed since times moved on/I'd give her my last dollar and now all she'll do is holler/oh my life has become a country song."
For the purists, the song may not be quite PC these days, but that didn't phase the Bombs.
"Typical of how we can when we hook up, we write 'It's Hard,'" says Crowell. "Hey, we can't be taking ourselves too seriously with this stuff. It's just fun you know."
"That was actually something Vince's father told him before he died," says Crowell, adding, "(Vince) told me the title, and I said 'let's do it'. We did it. My wife came home right about when we finished it, and we sheepishly played it for her, and she said she loved it. I didn't believe her, and I later heard her singing it in the shower. I called Vince and said it's okay to play for Amy (Grant) because I heard Claudia singing it in the shower."
"Both of us over the years have developed reputation as sensitive guys, but it's a pretty insensitive song. You can't take it too seriously."
The Cherry Bombs also include drummer Eddie Bayers, bassist Michael Rhodes, who toured with Emmylou Harris, pianist/organist Johnny Hobbs, who has been with Gill, guitarist Richard Bennett and guitarist Hank DeVito.
The origin of the Cherry Bombs is connected with Emmylou Harris. Crowell already was playing in her backing Hot Band. DeVito played with Harris as well.
Former Elvis sideman Glen D. Hardin had left Harris' backing Hot Band, and word got back to her that she "should at least audition me," says Brown in a phone interview from his office at Universal South Records, the label he in part owns and which is releasing his band's efforts.
"Her first three albums were three of my most favorite country albums ever," says Brown, a keyboard ace, who once toiled for Elvis. "I was more scared to audition for her than Elvis. I didn't even audition for Elvis. I did my best Glenn D. Hardin impersonation and got the job."
In stepped Brown and out went Crowell to go on his own.
Others playing for Harris included Ricky Skaggs, guitarist Albert Lee, bassist Emory Gordy Jr., Gill, Crowell and DeVito.
"I kept hearing on the bus Emmylou kept talking about Rodney," says Brown. "Rodney was producing Rosanne Cash's album, 'Right or Wrong.' He wanted to use pieces of the old Hot Band and pieces of the new Hot Band."
That resulted in Skaggs, Lee and Gordy Jr. playing on the disc.
"Rodney said, you know, we should go out and play some clubs," says Brown.
Next thing he knows is that the following Saturday night, Crowell was playing a gig in Redondo Beach, Cal. Gordy, Lee and DeVito were aboard with a billing of "Rodney Crowell, a boy and his hot band, the Cherry Bombs."
"We started playing up and down the coast, Santa Cruz, you name it any club," says Brown. "We would always have the press come out and see us and Ronstadt and Glenn Frey and Billy Gibbons (of ZZ Top). We go, 'this is working?'"
Crowell decided he wanted to use the Cherry Bombs on his second album, "But What Will the Neighbors Think," in 1980. Ace drummer Larrie Londin also was aboard as a Cherry Bomb.
They also recorded Crowell's next album "Rodney Crowell" and two more for Cash.