A SOFT GRIP MEDICAL CONNECTOR (10) COMPRISES A HOUSING (12,12',12") AND A FLEXIBLE MEMBER (80). THE HOUSING HAS A LUMEN EXTENDING THROUGH IT FROM AN UPSTREAM END (16) TO THE DOWNSTREAM END. A FLEXIBLE MEMBER (80) INCLUDES A VALVE PORTION (14) INTEGRALLY FORMED WITH A SLEEVE PORTION. THE VALVE PORTION IS POSITIONED WITHIN A SECTION OF THE HOUSING AND CAN CONTROL A FLOW OF FLUID THROUGH THE HOUSING LUMEN. THE SLEEVE (20) CAN BE INVERTED TO ENVELOPE SOME OR ALL PORTION OF THE OUTER SURFACE OF THE HOUSING. THE SLEEVE CAN INCLUDE A GRIPING PORTION INTEGRALLY FORMED WITH THE VALVE PORTION. THE CONNECTOR CAN ALSO CREATE A POSITIVE PRESSURE IN THE LUMEN UPON REMOVAL OF A SYRINGE OR OTHER MEDICAL FROM THE UPSTREAM END OF THE SUMMER.