We propose renewal of our program project for research into new and more powerful probabilistic direct methods solutions for the phase problem in biological crystallography. Our new objectives are methods that will be effective with single-wavelength data, at lower resolution, for larger structures. Such methods will expedite high-throughput biomolecular structure analysis, and will facilitate investigations of the structures of large, complex assemblies of biomolecules. The new methods will therefore have high impact in the genomics-proteomics- bioinformatics-structure-function-analysis-drug design paradigm of basic biomedical science. Our proposed project has four component projects: I. Direct Methods of Phase Determination II. Algorithmic Development for New Phasing Methods for New Phasing Methods III. Phases in Macromolecular Electron Crystallography IV. Phase Measurements for Macromolecular Crystallography Project I is focused on developing and testing new probabilistic phasing theory by a group led by Herbert Hauptman at HWI. Project II is focused on developing and implementing phasing practice in computer programs written, maintained, and distributed to the biostructural research community by a group headed by Charles Weeks at HWI and William Furey at the University of Pittsburgh. Project III is focused on direct methods phasing in electron crystallography using electron microscope images and diffraction data from thin microcrystals by a group led by Douglas Dorset at HWI. Project IV is focused on phasing using synchroton X-ray crystallographic techniques to exploit (1) Renninger three-beam interference effects to measure triplet phase invariants by a group led by Qun Shen at CHESS and (2) Bijvoet or Friedel pair amplitude differences from large structures with large numbers of anomalously scattering atoms measured with very high energy-resolution by a group led by Steven Ealick at MacCHESS and APS.