The present invention relates to an arrangement (1) pertaining to a compressive or clamp coupling (2) in which two mating sleeves (21, 22) act compressingly against an outer surface (23a) of a shaft (23), wherein the arrangement (1) is adapted to enable a first sleeve (21), an outer sleeve, to be displaced relative to a second sleeve, an inner sleeve (22), for instance when mounting the coupling The outer sleeve (21) has an inner conical surface (21a) and the inner sleeve (22) has an outer mating conical surface (22a) and an inner shaft-adapted cylindrical surface (22b), which is dimensioned to encircle said shaft (23) in the absence of an externally applied force and with a small tolerance, so that said sleeve can be displaced axially. The occurrence of forces acting between the inner cylindrical surface of the first sleeve and the outer cylindrical surface of the shaft caused by said clamping action shall be capable of providing a torque-transferring slip-free clamp coupling (2). At least one channel (26) is adapted to deliver lubricant media or oil under high pressure to and between said mating surfaces (21a, 22a). A first means (A) is active between the outer sleeve and the inner sleeve such as to cause the outer sleeve (21) to move axially in relation to the inner sleeve (22) in a first direction (R1) (or in a second opposite direction R2) at least when a lubricant pressure and a film has been established between mutually opposing and mating slide surfaces. According to the invention, the arrangement includes a second means (B), which is adapted to provide a reduction in and/or distribution of occurring end-related and radially active compressive forces on the cylindrical shaft surface (23a) or shaft section (23d) from the end-portion or end-portions of the outer sleeve (21) via an end-portion or end-portions of said inner sleeve (22).