"Stop Me If You Think You've Heard This One Before" was originally intended to be released as a single instead of "I Started Something I Couldn't Finish". However, the song contained the lyric "plan a mass murder" and it was banned from daytime airplay by the BBC due to the then-recent Hungerford massacre. Thus, the band decided not to release it in the UK; it was released in other regions, including North America, Europe, Australia and Japan.
A music video was produced by the director Tim Broad. It opens with a picture of the Oscar Wilde hanging on a brick wall, and features Morrissey and a group of Morrissey lookalikes cycling around Manchester, including famous locations such as the Salford Lads' Club.
The cover of the single is a picture of British actor and singer Murray Head from a still of the 1966 film The Family Way (a movie that would also be the source of the photograph on the cover of "I Started Something I Couldn't Finish"). There are four different versions of the cover, each tinted a different colour (red, orange, blue and grey) depending on the region.
In 2007, the song was re-composed as "Stop Me" with additional lyrics from the song "You Keep Me Hangin' On" by The Supremes by British DJ Mark Ronson featuring Daniel Merriweather on the vocals. Merriweather admitted in an interview with The Guardian that he was not very familiar with the original before he recorded Mark Ronson's revised version. He explained: "Mark said, 'I want you to sing on this – it's my favourite Smiths song,' so I listened to it. I'd heard it once before, but I was never a Smiths fan. But I thought it was beautiful." The song was later released as a single on 2 April 2007 on Columbia Records with the shortened name "Stop Me", and featured on the compilation album Version. The music video, released at the same time as the song, features a man who finds a pair of trainers that control him and force him to run along the motorway near the Blackwall Tunnel. This version was released in the United Kingdom. The international version showed people crying animated tears. Live versions by Mark Ronson and/or Stu Zender featuring Merriweather have appeared on Late Night with Conan O'Brien (on July 2007), BBC Radio 1 and Jimmy Kimmel Live!).
The single reached number two in the UK Singles Chart, number one in the UK Download Chart and gained considerable praise and reference, as well as controversy from loyal Smiths fans despite its chart success being the highest ever UK chart position for a Smiths song. The music review site ThisisfakeDIY gave the single a 5-star rating, citing that its popularity stemmed from its abstraction from a typical Smiths song, resembling a "sweeping, orchestral pop song with horns to boot … soulful, evocative vocals … a stirring mix". This song was number 80 on Rolling Stone's list of the 100 Best Songs of 2007.
It received a mixed review from musicOMH reviewer Jenny Cole, who remarked that the notion of "discoing up a Smiths track" was a "travesty", and queried that "Morrissey would no doubt hate the idea of someone who has previously worked with Christina Aguilera and Robbie Williams" re-composing his songs. However, despite such reservations, the reviewer remarked that despite its composition "in a mad way it works … Electronic, cheery and danceable, it's really not half bad" but that the addition of The Supremes to the song was "just mad".