A delivery system for delivering an endoluminal implant to a distal deployment location inside a body lumen from a proximal access location outside the lumen. The system includes the implant, a catheter, and a slidable sheath having an advanced position in which the sheath covers the implant and a retracted position in which the implant is exposed. The catheter includes a stabilizer having a distal end adjacent the implant proximal end and/or a catheter tip attached to a central core slideably disposed relative to the implant and having a proximal end adjacent the implant distal end. The catheter tip proximal end and/or the stabilizer distal end includes a docking section adapted to releasably engage a portion of the implant. Each docking section has an engagement geometry including a flared engagement surface that extends inside a short axial length of the implant or a pocket having a bottleneck geometry.