Poor Stewart Lee. Despite BBC Two’s best efforts to conceal the second series of his stand-up show, he finds himself more popular than ever, attracting audiences big enough to sustain a residency in London’s Leicester Square Theatre from now until the middle of February.

But such success does not sit easy on Lee’s weary shoulders, and it gives rise to a new catchphrase. ‘It’s not aimed at you,’ he repeatedly tells the Jimmy Carr fans finding their way into his audience, desperately trying to deter all but his hardcore demographic.

It’s all part of the way Lee’s fractious, intransigent elitism has become as much of an in-joke as his curmudgeonly harrumphs at other comedians – a self-awareness that softens his ‘passive-aggressive monotony’ without compromising it.

Yet for all his avowed desire to return to the days when he played to a devout cabal of middle-aged liberals, the first section of Carpet Remnant World is perhaps some of his most accessible, as he offers his cantankerous take on big news stories such as the assassination of Bin Laden – even including a few actual jokes in the mix. But Lee’s take on topical comedy is nonetheless more complex than the material that makes it on to Mock The Week – as his distinctive, tongue-in-cheek, version of Frankie Boyle’s gag about the Queen’s ancient vagina proves.

Nor can he do observational comedy with quite the conviction of a Michael McIntyre. He tries with limited success – hence the material about shops with ‘world’ in their name – but eventually throws his hands up in defeat, acknowledging this is a fragmented, out-of-touch show. His life now involves only driving to gigs and looking after his four-year-old son.

In sarcastic commentary on fellow middle-aged comics, he has to concede that his viewpoint has drastically narrowed as the range of influences and experience shrinks to the mundanely domestic. After all, what comic could possibly find enough mileage in Scooby Doo And The Pirate Zombie Jungle Island to fill an extended routine?

Well, Lee could obviously. A gloriously self-referential rant about the ghost-hunting teenagers remains awkwardly funny while providing a sharp satire on the irrelevance of most comedy. It fits in with the ethos of the show in exposing the tricks of the modern stand-up trade, such as tear-jerking through lines or the structural devices to make disparate routines seems like they are true to a theme.

The next disparate routine here is a convincing argument about how the likes of Twitter have reduced us to a surveillance society, with his every move being noted and commented upon. It leads to a catalogue of viciously vitriolic abuse Lee has sustained by online trolls wishing him harm. He’s not the first comedian to have made capital from his critics, but it is very effective, set to a inappropriately relaxing jazz soundtrack.

Maybe parenthood has softened him a little, as Carpet Remnant World is less intense and less challenging than some of his more powerful shows – and less reliant on the repetition and pregnant pauses, too. But it’s no less funny, nor less thoughtful, for it – appealing both to both the comedy anoraks who are Lee’s core audience and, whisper it quietly, new converts. If all goes horribly wrong, this could make his fan base expand again.