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The opportunities to use dielectric Photonic Crystals (PhCs) as the media of cylindrical invisibility cloaks, designed using Transformation Optics (TO) concepts, are investigated. It is shown that TO-based prescriptions for radial index dispersion, responsible for turning waves around hidden objects, can be dropped, if PhC media support self-collimation of waves in bent crystals. Otherwise, to provide prescribed anisotropy of index dispersion, it is possible to employ PhCs with rectangular lattices. It is found, however, that at acceptable cloak thicknesses, modifications of crystal parameters do not allow for achieving prescribed level of index anisotropy. This problem is solved by finding reduced spatial dispersion law for radial index component, which is characterized by decreased against TO-prescriptions values near the target and increased values in outer layers of the cloak. The cloak utilizing reduced prescriptions for indices is shown to perform almost as efficient, as TO-based cloak, in terms of both wave front restoration behind the target and reducing total scattering cross-width of the target.