A mattress and pile of domestic rubbish was set alight in an alleyway in Rotherham.
Firefighters were alerted to the blaze on Harrison Street, Holmes, at 10pm on Monday.
They prevented the flames from spreading.
Crews also dealt with a pile of rubbish set alight behind a derelict property on Churchill Avenue, Maltby, Rotherham, that night.
Witnesses or anyone with any information about the culprits should call South Yorkshire Police on 101.