A Wendy House, part of a fence and a tarpaulin were all damaged by a blaze which officers say appears to have been deliberately set in the garden of a house in Beddie Crescent.
It happened sometime between last Thursday and Monday,
All the property was damaged although not destroyed as a result and the fire seems to have burnt out.
Meanwhile, in another incident, a bug hut in the garden of a house in Church Lane in Wigtown was totally destroyed, again as the result of a fire which appears to have been set deliberately.
It was discovered at 3 am on Tuesday.
Constable Andrew Osborne, at Newton Stewart, said: “This appears to be a worrying trend and it is very lucky neither of these fires have spread to other properties. Again the act of setting a deliberate fire is a totally reckless act and could have catastrophic consequences.”
Anyone with information is urged to call police on 101.