The song was written as a tribute to the Pixies, a band that had an important influence over Radiohead at the time. Its also one of Radiohead's oldest songs; it was created when the band was still known as 'On A Friday' (pre 1991).
'Stop Whispering' clinched the band's relationship with the management team of Hufford and Edge. Chris Sheldon remixed it for a United States release; that version features strings and has a slower tempo.
The best version of this song, however, is the live one. Thom adds a few lyrics to the ending. A live version can be found on the High and Dry Live Package, which contains a closing 'fuck you'.