Hyperboloidal initial data sets do not generally evolve into spacetimes with a well-defined Scri unless they satisfy the shear-free condition. In this talk we present a procedure for gluing shear-free hyperboloidal initial data which leaves the conformal infinity connected. Our work is done within the framework of weakly asymptotically hyperbolic metrics, and a special attention is paid to the shear-free condition. This is a collaboration with Paul T Allen, James Isenberg and John M Lee.