Police have been searching an area stretching from the scene of the shooting to the farm where he was found, including about 13km of riverbank along the Ashburton River.
Today they said a black mountain bike and a number of personal items thought to belong to Tully had been found.
However, they were continuing to look for any other items, which could include another firearm and ammunition, which may have been in his possession.
Police will continue their search tomorrow.
They are also still seeking information about the owner of a blue, red and yellow Challenger Sport mountain bike recovered last week.
The funeral for Leigh Cleveland was held in Alexandra yesterday. Peg Noble's funeral will be held in Ashburton tomorrow.