Compliant anastomosis system utilizing suture

A surgical method for connecting a graft vessel having a lumen therethrough to a target vessel having a lumen therethrough, where both the graft vessel wall and the target vessel wall provide natural hemostasis relative to blood flowing therethrough, the method comprising:

• providing an integrated anastomosis tool;
• moving said integrated anastomosis tool into proximity with the target vessel;
• creating only a single opening in the target vessel wall with said integrated anastomosis tool;
• placing the end of the graft vessel in proximity to the single opening in the target vessel wall such that the end of the graft vessel defines a perimeter around the single opening in the target vessel wall;
• suturing the end of the graft vessel to the side of the target vessel with said integrated anastomosis tool such that fluid can flow through the single opening in the target vessel wall into the lumen of the graft vessel, and such that hemostasis is substantially restored;
• maintaining the graft vessel completely outside of the single opening in the target vessel during said placing and said suturing;
• and
• withdrawing said integrated anastomosis tool away from the target vessel, wherein during said withdrawing the entirety of said integrated anastomosis tool is maintained outside the lumen of the graft vessel.