A turning tool including a basic body having a pocket, a shim plate mounted in the pocket, and an indexable turning insert mounted in the pocket. The pocket opens in a front surface and in a side surface of the basic body, and accommodates two spaces spaced-apart level-wise, a lower space housing the shim plate and delimited by a bottom surface and two side support surfaces, which form an acute angle with each other, one of which is a primary side support surface and the other one a secondary side support surface, and an upper space housing the turning insert. The shim plate includes an upperside and an underside between which a pair of primary and secondary contact surfaces extend, which form an acute angle with each other and are urged against the primary and secondary side support surfaces in the pocket, as well as a pair of inactive surfaces extend in the form of an outer end surface and an outer side limiting surface, which together delimit a supporting corner section of the shim plate. The turning insert has a triangular basic shape and includes an upperside, an underside resting against the upperside of the shim plate, and three side surfaces that are situated in a first imaginary, equilateral triangle and therefore converge in pairs at an angle of 60° toward corners in which cutting edges are included. First and second tightening elements are arranged to detachably fix the shim plate and the turning insert individually. The secondary side support surface of the pocket is formed on a lug having a top surface situated under the turning insert. Respective acute angles (ε, γ) between the primary and secondary side support surfaces of the pocket, and the primary and secondary contact surfaces of the shim plate, are smaller than 60°. The underside of the turning insert and the upperside of the shim plate are engaged with each other via an interface that includes female-like and male-like engagement members, which are in engagement with each other to prevent turning of the turning insert.