A system and method for determining the genetic data for one or a small set of cells, or from fragmentary DNA, where a limited quantity of genetic data is available. Genetic data for the target individual is acquired and amplified using known methods, and poorly measured base pairs, missing alleles and missing regions are reconstructed using expected similarities between the target genome and the genome of genetically related subjects. In accordance with one embodiment of the invention, incomplete genetic data from an embryonic cell is reconstructed using the more complete genetic data from a larger sample of diploid cells from one or both parents, with or without genetic data from haploid cells from one or both parents, and/or genetic data taken from other related individuals. In accordance with another embodiment of the invention, incomplete genetic data from a fetus is acquired from fetal cells, or cell-free fetal DNA isolated from the mother's blood, and the incomplete genetic data is reconstructed using the more complete genetic data from a larger sample diploid cells from one or both parents, with or without genetic data from haploid cells from one or both parents, and/or genetic data taken from other related individuals. In one embodiment, the genetic data can be reconstructed for the purposes of making phenotypic predictions. In another embodiment, the genetic data can be used to detect for aneuploides and uniparental disomy.