A method is introduced to miniaturize invisibility cloaks by 50% using wave tailoring and finite/non-zero wave impedance of double near zero (DNZ) slabs. Unlike previous works, which use thick dielectric matching layers to miniaturize internal cloaks, the proposed technique is applied to both internal and external cylindrical cloaks using a thin and short DNZ slab to change cloaks' shapes to half-cylinder shells. Moreover, sets of structures are introduced for the half sized cloaks to enable using feasible-to-fabricate structures with the help of a rigorous theoretical analysis, which is validated via full-wave simulations. All of the presented results show that the proposed half cloaks can function perfectly well. The sensitivity of half-sized cloaks to the length and material properties of the DNZ slab is investigated to find the shortest length and the highest values of the permittivity and permeability for the slab to have small yet realizable structures. The analysis shows that slabs with length as small as the diameter of the cloaks and constitutive parameters (permittivity and permeability) as high asεslab=μslab=0.1-0.1iand εslab=μslab=0.05-0.04i for half-sized external cloaks and half-sized internal cloaks, respectively, can still considerably reduce the scattered fields. The effect of the loss and incident angle of the field on the performance of the miniaturized cloaks are also analyzed.