A container for carrying a medical instrument such as an endoscope after use and before cleaning, comprises a perimeter wall having a height h and defining an enclosure with a diameter d. The perimeter wall is substantially rigid in the height dimension. A flexible base and a flexible cover are attached to the wall. The wall is compressible to a reduced diameter configuration for storage and expandable to an increased diameter configuration for use. The wall may comprise a series of adjacent panels foldable concertina-style to reduce the diameter.