Yet the group's main man, Chris Difford, reckons he has only now accepted how the group should work – despite the number of classic hits he has written.
"It's only been in the last five years that I have accepted myself," says Chris, who brings the band to the O2 Academy in Glasgow next month.
"We have good foundations in the band now and you realise everything else will follow from there.
"I understand more about being in a band now than I have ever done before in some ways; it's about knowing everybody's space in the band and allowing everyone's creativity to flow, even if that is something you do not particularly like doing."
For years Chris and co-front man Glenn Tilbrook have fronted Squeeze, as well as their Difford and Tilbrook project in the 1980s.
Their brilliant hits have included Up The Junction, Cool For Cats and Annie Get Your Gun.
Now they are out on the road again, this time with Squeeze's Pop Up Shop tour, which sees CDs of each night's concert available to buy immediately after the gig ends, along with a new EP.
For Chris, there is an urge to start playing new material, and he is hopeful there will be a new Squeeze album in 2013, their first featuring fresh songs for 15 years.
"If you do the same show each time you tour you will always get a great crowd coming to see you, but it is basically doing the same play every time," he explains.
"Whereas if you twist the plot a bit, then people are intelligent enough they can enjoy the new songs and the new way we do our shows."
That is just the first step as the group gear up for the future.
"We have some new material and we will start recording a new album next year," he says.
"We have not formally discussed it yet or the timings, but we just need to sit down and work out how to achieve it. There is no rush though, but I think when people in Glasgow hear the new songs they will be pleasantly surprised."
Chris seems content with how things are with Squeeze now as the band approach five years since reuniting, having split in 1999.
"A band is like a family, so there is always a lot of unsaid resentment there," he says.
"Then you realise resentment and burning bridges is pointless, and that you should take it a day at a time."
That is not to say the 58-year-old has lost all his fire, though. Squeeze spent part of this summer on tour in America, mainly with the B-52s.
While the jaunt with the oddball party band was a "great experience", Chris and company also found themselves playing the Coachella Festival in California. But it is clear this was most definitely not a great experience.
"Coachella was like playing at a golf club," he says.
"It was not a festival I warmed to particularly and I didn't enjoy it. It's just not like the British festivals where there is a massive vibe that you can feel, it's very different out there.
"We were whisked in and out without seeing any other bands, which is probably why I did not feel that great about it as I did not have time to mosey around and enjoy it."
l Squeeze, O2 Academy, December 9, £32.50, 7pm.