I Should Coco

Sam Williams produced the album at Sawmills Studio in Cornwall, with John Cornfield engineering. The band came back to Sawmills to finish it after signing to Parlophone. Williams set the amplifiers in the same room as the players and let some sound bleed into the drum microphones, and most basic tracks took one or two takes. Quinn said the whole record took about three and a half months and cost less than the video for Alright.

Some tracks changed shape on the second visit. Lenny was sped up from a slower take, with bass and guitar re-recorded over the faster drums, and We're Not Supposed To grew out of a four-track home demo. On Sofa (of My Lethargy) Williams played bass and a friend added Hammond organ, while Quinn moved to guitar and Coombes to piano. Coombes said the band made the album quickly to catch the energy of the songs on tape. The bell chimes that end Strange Ones were recorded at Carfax Tower in Oxford. The title is Cockney rhyming slang for "I should think so", and the cover is a painting by the Moody Painters of Oxford's Cowley Road, and the sleeve was assembled by The Designers Republic.

It reached number one on the UK chart for three weeks and sold more than a million copies worldwide. Singles were Caught by the Fuzz, Mansize Rooster, Lose It (a US vinyl release on Sub Pop), Lenny and Alright/Time. NME's Steve Sutherland gave it nine out of ten and wrote "These freaks shall inherit the earth." It was nominated for the 1995 Mercury Prize. A 20th anniversary reissue appeared on Parlophone on 27 November 2015.