A technique manages a virtual hard disk tree in a computing system executing a hypervisor to provide a client virtualization environment. The technique involves linking, by a client executing within a control virtual machine of the client virtualization environment, a first delta image of a virtual hard disk generated later in time to a base image of the virtual hard disk. The technique further involves modifying contents of the first delta image, the base image, and a second delta image which is linked to the base image; and deleting the second delta image after modifying the contents of the first delta image, the base image, and the second delta image. The base image and the first delta image, together with additional delta images of the virtual hard disk comprise a tree of images of the virtual hard disk.