Burglaries of two homes in Mildenhall are being linked to two further incidents of criminal damage.
All four incidents took place overnight between Tuesday, February 5, and the next day, in Heathland Way.
The suspect got into the first house through an unlocked downstairs window, but no items were stolen.
The second home was burgled at around 3.15am through an unlocked rear door.
One of the occupants heard the door open and challenged the intruder, who fled and was seen climbing over a fence into College Heath Road and running into the housing estate opposite.
The suspect was described as a white man, around 5ft 9ins, of medium build, with a black beard/heavy stubble and an English accent.
Police are linking the burglaries with two reports of damaged security lighting.
Anyone with information should call 101 or Crimestoppers on 0800 555 111