A method and packaging system for forming a sealed vacuum package having minimal residual air remaining. At least one vacuum lance is provided in the interior of a partially-formed package to withdraw the air, the package being closed on three sides and having a fourth side open for insertion of the vacuum lance. An air restriction can be provided along the fourth side to form a closed edge that prevents ingress of air into the package interior after the evacuation of air. In one aspect, the air restriction may comprise a pair of pinch rollers that compress the package at the fourth side edge to form a pinch seal that provides a relatively airtight air chamber inside of the package prior to and during sealing of the package. In another aspect, the air restriction may comprise a partial seal formed around the lances to prevent or minimize air from reentering the package. In yet another aspect, the air restriction may comprise a compressed air seal formed by an air compression device that keeps the ends of the film pressed together.