Black Lips are a band of intoxicating contradictions. They are the peace-loving last gang in town. They are ultra-puerile super-literates. They are trailblazers - touring the territories other bands fear to tread, ranging from post-Arab Spring Egypt to Iraq - yet they are unabashedly capitalist, working on their own range of denim. Musically they look back to Nuggets, The Monkees and Tone Loc, yet lyrically they flash forward to the projected effects of social media and sing love songs that involve setting your mobile on vibrate. They were brought up on punk rock yet despise the morass of rules it has become. Their brutal homage to Deliverance with the video for 'Boys In The Wood' would make you assume they're a bunch of "redneck meth-heads", yet their cerebral attention to showmanship even extends to creating a scent to add a fourth dimension to their live shows. Their songs are both daft and disposable, and either instant or insidious.

Ultimately, they are neither throwbacks nor throwaway. For a seemingly bratty band that has historically loved to shoot off at the mouth, they have a keen sense of where they want to be on the rock canon. On the last record, 2011's Arabia Mountain they made an unlikely and unholy union with superstar pop producer Mark Ronson. For their latest and seventh album Underneath The Rainbow (stream it in full below), out on Vice Records on March 17, they've been recorded by Patrick Carney of the Black Keys and Tommy Brenneck, musical director of the Dap-Kings, and been snapped by the incomparable Mick Rock.

Rumour has it they had attempted to procure from penitentiary the production skills of one Phil Spector, one case where a performance would literally have to be phoned in. But was that another white lie from the lips of the Lips, masters of their own self-mythology? While last time we met, bass player and vocalist Jared Swilley was concerned with helping me get guitarist Cole Alexander to make a plastic toy guitar meet its end on a window sill, this time he broke down perceptions of a pleasingly perplexing band.

How true is that that you wrote letters to Phil Spector thing asking him to produce you?

Jared Swilley: Cole was really trying to do that. You know Phil Spector and Joe Meek are two of my favourite producers of all time but not only would it be a logistical nightmare trying to get someone to produce your album over a phone from prison, where they probably only get 20 minutes a day, it would have been tacky, because the reason we would have been using him would have been for his infamy and not for his wonderful production skills, because Phil Spector's not what he was in the 60s or even the 80s. I mean even the last album Cole was talking to Charles Manson about getting him to write some lyrics. I don't want to use someone as negative as an instrument for us to have a good headline.

Last time you used Mark Ronson, this time it's Patrick Carney and Tommy Brenneck – do you have a list of producers you want to work with?

JS: The reason we wanted Mark in the first place was because we never wanted to work with a producer, so the last time around, we sent Vice just this insane list of all the A-list producers in the world, thinking it wouldn't work but Mark actually wanted to do it. We were supposed to do it with him this time around and we had rented a place in London for a month and two days before Mark had to postpone for a while because he's working with Beyonce and all these huge people. But we didn't want to postpone so we just called Tommy because he works with Mark a lot with Daptone stuff and did stuff with Amy Winehouse and we liked his ear and we liked his studio. And we played in Mexico City with Black Keys and in just late night drunk talk, Patrick was like, "that sucks, I'd like to produce some stuff", so it just worked out like that.

How did the two compare in styles?

JS: Tommy's more about tones, he has a really incredible ear for drums and horns and guitar tones and all that. A lot of the stuff we did with him the songs were already written, whereas when we went in with Patrick we brought more skeletal structures of songs so we kind of built them while we were in the studio.

I like 'Dog Years' the best because Cole has this monologue that closes out the album. There's this really weird gay rockabilly guy from the 60s called Stud Cole who did all these monologues and it was based on that.

Watching Cole do that speech I had to bite down on my hand because I didn't want to make him nervous because I was laughing so much. He was doing it with such conviction – and really pouring his heart into it. It was really endearing watching him do that.

And you used Mick Rock to take your photo for the album.

JS: Yeah that was so awesome. The way he shoots is very intense to put it lightly. I wanna put a video out because I had one of my friend's film it – basically it starts off like this: "Come on Cole. Come on Jared. You fucking cunt. You fucking cunt. You fucking rent boy. You've been a rent boy your whole life, you have your dick so far down your mother's arse and you have my spunk all over my face. Ok, I'm done." It was really amazing. Growing up, when I first got into a lot of stuff, I didn't know who Mick Rock was. I knew all his pictures and just the amount of important stuff just in pop culture history – he just captured some of the most iconic images of the 20th-century as far as music goes.

Musically your sound is retro, but lyrically it's very modern – tell me about 'Justice After All' and its commentary on social media…

JS: It's weird how nowadays people cultivate what they want their public persona to be even if they're a regular person. That's never happened in human history so it's weird. I'm not gonna say its bad. It's just a commentary on that and how just internet and social media has made the human race have ADD because no one can sit down and read – I bet there's very few people who could go and read Proust for an evening. Things move so fast now. It's completely changed. I have to fight it all the time. Sometimes I have to drive my computer to our practice space and leave it there so I can get reading done.

I read you've got a fragrance planned, what does it smell like?

JS: The first one was synthesised female hormones - we put that out and it was too potent and kind of made everyone a little sick so we had to go back to the drawing board. Now it's more this kind of cedar musky kind of smell – like a dad or grandpa smell. It's gonna take you back to a familiar time so we're attacking people's sub-consciousness.

A few years ago I was dating this girl and her brother had to sell synthetic meat smell. I was like, wow, that's like 4D. And so I kept thinking about that and I met a guy in France that makes those machines and we've been working with him. We actually get to use it for the first time tomorrow night so we will see how it goes. Our records are gonna smell like that too.

We want to cater a sense to every song - we have a song called 'Drugs', so we want kind of a weed smell, and we have a song called 'Dumpster Diving', so we wanna recreate a smell of wet garbage. We have a moon scent which is crazy, because nobody knows what the moon smells like. Out of the 13 people that have gone to the moon they have to wear helmets. If they weren't wearing their helmet their head would explode so no one knows what the moon smells like.

I guess next tour we'll be working on taste somehow.

You seem like a band of contradictions - how much do you revel in that?

JS: This French company approached me and said, do you wanna design a jacket, and I was like, oh yeah, that sounds cool. so I drew up this jacket and wrote a song about this imaginary gay biker gang called The Pink Angels and that song's gonna come out on a flexi disc which will be packaged with the jacket.

The thing is, we're not like ideologues or anything, we just do what we wanna do.

I'm not really into uptight people. The reason I got into punk rock was because I hated rules and then when I was a teenager I started going to punk shows there were all these rules – you had to be a communist and a vegan and there's all these things and I'm like, just fucking chill out, we're all gonna die in a couple of decades, so why don't you just have a good time. And every time you try to take a stand on something, all the time you know, you're going to contradict yourself at some point.

We don't really have a lot of scruples with stuff except having fun.