The invention relates to a cutting tool of the type that comprises a replaceable cutting insert (2) and a basic body (1), which includes a rear fixing part (5), a front supporting part (6), and a tightening part (7) situated over the support part. The tightening part (7) is spaced-apart from the two other parts (5, 6) via two gaps (8, 9) and connected to the rest of the basic body via elastic material portions (26) that form a joint for the tightening part. In such a way, the tightening part can be pivoted and clamp the cutting insert by means of a tightening element (27). In a known way, the fixing part (5) comprises an internal channel (13) for feed of a cooling liquid or fluid in the forward direction through the basic body (1). According to the invention, the channel (13) extends into a second channel (32) inside the tightening part (7) via a channel section (33) that is entirely or partly housed in a bridge (28), which, like the joint, is formed of the material in the basic body, and which bridges one (9) of the two gaps. In a second aspect, the invention also relates to a basic body for cutting tools of the kind in question.