ABSTRACT Joint statistics of periods and mass ratios of close binaries and its dependence on primary mass can be explained by assuming that seed binary companions are formed by disc fragmentation at random intervals during assemblage of stellar mass and migrate inwards as they accrete from the circumbinary disc. A toy model based on simple prescriptions for the companion growth and migration reproduces such aspects of close solar-mass binaries as the distribution of binary periods P, the brown dwarf desert at short P, the nearly uniform distribution of mass ratios, and a population of equal-mass binaries (twins) that decreases linearly in frequency with log P. For massive stars, the model predicts a large fraction of early mergers, a distribution of log P with a negative slope, and a mass-ratio distribution that is also uniform but with a substantially reduced twin fraction. By treating disc fragmentation as a stochastic process, we also reproduce the observed properties of compact triples. Success of our toy model suggests that most close binaries and compact triples indeed formed by disc fragmentation followed by accretion-driven inward migration.