We analyze the diffraction characteristics of dielectric gratings that feature a high index grating layer, and devise, through rigorous numeri-cal calculations, large bandwidth, highly efficient, high dispersion dielectric gratings in reflection, transmission, and immersed transmission geometry. A dielectric TIR grating is suggested, whose −1dB spectral bandwidth is doubled as compared to its fused silica equivalent. The short wavelength diffraction efficiency is additionally improved by allowing for slanted lamella. The grating surpasses a blazed gold grating over the full octave. An immersed transmission grating is devised, whose −1dB bandwidth is tripled as compared to its fused silica equivalent, and that surpasses an equivalent classical transmission grating over nearly the full octave. A transmission grating in the classical scattering geometry is suggested, that features a buried high index layer. This grating provides effectively 100% diffraction efficiency at its design wavelegth, and surpasses an equivalent fused silica grating over the full octave.