A tool intended for chip removing machining is disclosed. The tool is of the type that has a basic body and an indexable cutting insert that can be connected to the basic body via an interface including a primary connecting surface in the basic body and a secondary connecting surface in the cutting insert. Among two cooperating support flanks included in the connecting surface of the basic body, one is situated on a level above the other in order to form a lateral support for the cutting insert. In the connecting surface of the cutting insert, contact flanks are included that, together with the clearance surface of the cutting insert, form a V-shapedly converging wedge part that can be applied in a seat delimited by the support flanks, the contact flank being urged against the low-positioned support flank of the basic body, while an upper part of the clearance surface of the cutting insert is urged against the high-positioned support flank. By means of the high-positioned support flank, large cutting forces can be carried in a dominant line of action, the interface in other respects efficiently counteracting such tendencies to dislodging/turning of the cutting insert that are caused by more moderate forces in other lines of action. In addition to the proper tool, a cutting insert and a basic body for the tool, per se, are also disclosed.