It is expected that a correctly phased low-resolution synthesis would show a set of isolated 'blobs' located near to the centres of the macromolecules if the corresponding cut-off level is chosen properly. This is not always the case when using experimentally measured structure-factor magnitudes. Nevertheless, this property can be efficiently used as a constraint in the low-resolution ab initio phasing of structure factors. The suggested procedure consists in generating a large number of random phase sets, selecting those that together with the observed magnitudes result in the desired number of blobs in Fourier syntheses, and averaging the selected phase sets. The current paper discusses the formal definitions, analysis of low-resolution syntheses, some phasing algorithms and their application to ab initio phasing.