Implant delivery sleeves having non-tapered tubular walls with constricted implant delivery channels for inserting implants into tissue pockets

An implant delivery sleeve comprises a tubular wall having a proximal end with a proximal opening, a distal end with a distal opening, and an implant delivery channel extending between the proximal and distal ends of said tubular wall. A plurality of bands interconnect portions of the tubular wall for constricting the implant delivery channel adjacent the distal end of the tubular wall. As an implant is advanced toward the distal end of the tubular wall, the constriction squeezes and/or deforms the implant for facilitating insertion into an incision that is smaller than the normal size of the implant.