A container (10) is provided for housing a medical accessory (20), such as a valve of a flexible medical endoscope, during processing (cleaning and high level disinfection) thereof following its use on a patient. The container (10) has a closure mechanism (15) comprising first and second complementary members (16, 17) adapted to engage with one another. Once engaged, the first and second complementary members (16, 17) cannot be disengaged from one another without the container (10) breaking. The container (10) is thus suitable only for single use, so as to prevent cross-contamination, and to comply with appropriate public health guidelines.