A drillstring for drilling a borehole through an earth formation, comprising: a length of drillpipes; and a bottomhole assembly (BHA,300) disposed at a downhole end of the length of drillpipes, the bottomhole assembly comprising a transition section at the downhole end of the length of drillpipes, wherein: the transition section is configured to reduce vibration of the bottomhole assembly during drilling; the transition section varies gradually in acoustic impedance between the acoustic impedance of the drillstring above the transition section and the acoustic impedance of the bottomhole assembly below the transition section; the transition section comprises an upper tubular and a lower length of separably joinable elements; in order to gradually vary the acoustic impedance, the lower length of separably joinable elements increases in outer diameter in a step-wise fashion at each joint or at each second joint between the separably joinable elements with distance from the downhole end of the length of drillpipes; the upper tubular has an inner diameter that is greater than an inner diameter of the lower length of separately joinable elements and less than an inner diameter of the downhole end of the length of drillpipes; and the transition section forms at least 30% of a total length of the bottomhole assembly (BHA,300); characterized in that the outer diameter of the lower length of separably joinable elements increases linearly along the transition section with distance from the downhole end of the length of drillpipes. a length of drillpipes; and a bottomhole assembly (BHA,300) disposed at a downhole end of the length of drillpipes, the bottomhole assembly comprising a transition section at the downhole end of the length of drillpipes, wherein: the transition section is configured to reduce vibration of the bottomhole assembly during drilling; the transition section varies gradually in acoustic impedance between the acoustic impedance of the drillstring above the transition section and the acoustic impedance of the bottomhole assembly below the transition section; the transition section comprises an upper tubular and a lower length of separably joinable elements; in order to gradually vary the acoustic impedance, the lower length of separably joinable elements increases in outer diameter in a step-wise fashion at each joint or at each second joint between the separably joinable elements with distance from the downhole end of the length of drillpipes; the upper tubular has an inner diameter that is greater than an inner diameter of the lower length of separately joinable elements and less than an inner diameter of the downhole end of the length of drillpipes; and the transition section forms at least 30% of a total length of the bottomhole assembly (BHA,300); characterized in that the transition section is configured to reduce vibration of the bottomhole assembly during drilling; the transition section varies gradually in acoustic impedance between the acoustic impedance of the drillstring above the transition section and the acoustic impedance of the bottomhole assembly below the transition section; the transition section comprises an upper tubular and a lower length of separably joinable elements; in order to gradually vary the acoustic impedance, the lower length of separably joinable elements increases in outer diameter in a step-wise fashion at each joint or at each second joint between the separably joinable elements with distance from the downhole end of the length of drillpipes; the upper tubular has an inner diameter that is greater than an inner diameter of the lower length of separately joinable elements and less than an inner diameter of the downhole end of the length of drillpipes; and the transition section forms at least 30% of a total length of the bottomhole assembly (BHA,300); characterized in that the outer diameter of the lower length of separably joinable elements increases linearly along the transition section with distance from the downhole end of the length of drillpipes.