In this chapter, we consider several ideas that might lead to improved reconstructions in coherent diffraction imaging. To avoid the conditions that render the inverse problem ill conditioned, and the usual iterative algorithms nonconvergent, we consider approaches that entail (1) a modification of the sample preparation, (2) a new experimental modality, which uses a noniterative holographic Hilbert transform method to reconstruct the image, or (3) a geometric Newton-type algorithm. The final section describes the detailed implementation of the holographic Hilbert transform method. All of these proposals are illustrated with numerical experiments.