Previously [Courtial et al., Opt. Express 26, 17872 (2018)] we presented the theory of transformation optics (TO) with ideal lenses and demonstrated an example, an omnidirectional lens. Here we interpret this omnidirectional lens in two different parameter regimes as ideal-lens cloaks that employ different cloaking strategies: a standard "shrink cloak" in which objects appear smaller (ideally zero) and a novel "abyss cloak" in which interior physical-space positions are mapped to the exterior and thus are visible only from certain directions. We proceed to combine two nested abyss cloaks into another novel, omnidirectional, "bi-abyss cloak." Our work significantly extends the arsenal of cloaking strategies.