We recently presented what we believe are new cloaking strategies [Belin et al., Opt. Express 27, 37327 (2019)], abstracted from the properties of an ideal-lens cloak that exists in theory only. Key to the cloaking strategies is that objects on the cloak's inside are imaged to its outside. In the simplest case, interior objects appear simply shifted, forming a "shifty cloak". Here we connect our work to several previous investigations of shifty cloaks and other shifty devices, designed using standard transformation optics, thereby bringing our cloaking strategies closer to experimental realization. We investigate to the best of our knowledge novel combinations of shifty cloaks, specifically Janus devices and optical wormholes. Finally, we demonstrate an experimental realization of a paraxial shifty cloak.