An escrow module of a valuable media depository is configured to self-adjust the position of an escrow drum relative to an escrow pinch. The media is maintained within the pinch as the escrow module takes in media items and returns media items by the self-adjusting positions of the escrow drum. As the drum fills up with media items, the drum is moved away from the escrow pinch while maintaining a consistent media path and providing consistent performance regardless of the number of media items being processed in a transaction to and from the drum.