A system for collecting and compressing waste collected in a medical or surgical procedure. The system includes a bag for collecting the waste that is seated on a mobile cart. Once the waste is collected the bag is closed and, while on the cart, transported to a compactor. While on the cart, the bag is compacted. Air in the bag is discharged through a one-way valve fitted to the bag. The one way valve may be attached to a cartridge that is inserted into the bag opening. The air discharged from the bag is filtered prior to discharge into the ambient environment. The filter may be built into the one-way valve.