A luminal access system comprises an evertable, lubricious sleeve, a pusher tube, and optionally a lumen tube. The evertable, lubricious sleeve is attached to a non-evertable sheath which is coaxially received over the pusher tube. A distal portion of the evertable sleeve folds or everts into an axial passage of the pusher tube where it is connected to a lumen tube. A distal portion of the pusher tube may be bendable, typically comprising a relatively soft polymer which is circumferentially reinforced to enhance hoop strength.