The song was produced by Lipsey, McVey and Simm. It received strong reviews from music critics. The track is one of the group's darkest and most haunting singles to date. The lyrics describe escaping from the reality and harshness of the world, possibly an abusive relationship (you never seem to wonder/how much you make me suffer). It was released as the third single from the group's debut album One Touch in April 2001 and sold 64,242 copies. In 2007, Czech singer Tereza Kerndlová covered the song as "Zhasis" for her album Orchidej.
According to tunebat.com, the song is in the key of E minor and played at a tempo of 106 BPM.[2]
^Run for Cover (UK cassette single sleeve). Sugababes. London Records. 2001. LONCS459.{{cite AV media notes}}: CS1 maint: others in cite AV media (notes) (link)
^Run for Cover (European CD single liner notes). Sugababes. London Records. 2001. 8573 87771 5.{{cite AV media notes}}: CS1 maint: others in cite AV media (notes) (link)
^Run for Cover (UK DVD single liner notes). Sugababes. London Records. 2001. LODVD459, 8573 88022 2.{{cite AV media notes}}: CS1 maint: others in cite AV media (notes) (link)
^Run for Cover (Australian CD single liner notes). Sugababes. London Records. 2001. 8573 88020 2.{{cite AV media notes}}: CS1 maint: others in cite AV media (notes) (link)