A trocar assembly (100) includes a trocar (102) that includes a trocar housing (114) and a cannula that extends distally from the trocar housing, and an integral seal system (306) positioned within a central passageway (308) extending axially through the trocar and engageable against a surgical tool shaft extended therethrough. The integral seal system includes an asymmetric seal and a duckbill seal arranged distal to the asymmetric seal, and the asymmetric seal defines a diaphragm that complements insertion and extraction drag forces generated by the duckbill seal against the surgical tool shaft such that total insertion and extraction drag forces generated by the integral seal system are equalized.
