Oil fell to around $65 a barrel on Tuesday, pressured by the possibility that U.S. shale oil producers could increase drilling activity and by a stronger dollar. U.S. drillers cut the number of rigs by just one last week, data showed on Friday, and Goldman Sachs said prices were at a level that would spur activity. The dollar could rally further, Morgan Stanley said, adding to a growing list of headwinds crude faces that include rising OPEC supply.