There is a great need for methods for non-invasive prenatal testing (NIPT). Non-invasive prenatal testing can be used to test for many conditions; for example, it can be used to determine paternity of a gestating fetus, to determine Whether or not a fetus has any Whole chromosomal abnor malities such as DoWn syndrome, EdWards syndrome, or Turner Syndrome, to determine Whether or not a fetus has any partial chromosomal abnormalities such as mosaicism, dele tion syndromes, or duplications, or to determine the genotype of the fetus at one or a plurality of loci, for example disease linked single nucleotide polymorphisms (SNPs) or short tan dem repeats (STRs). [0004] Non-invasive prenatal testing is typically done by measuring fetal DNA that may be present in maternal blood. Recent efforts have focused on isolating fetal cells that may be present in maternal circulation, or on measuring cell free DNA (cfDNA) that is present in the maternal plasma, and Which contains a mixture of maternal DNA and fetal DNA. Methods that focus on measuring cfDNA are affected by the fraction of fetal DNA that is present in the maternal plasma. Different methods of measuring the fraction of fetal DNA in the maternal plasma give different results, but typically the percent of DNA that is from the fetus out of the total amount of DNA (fetal fraction, FF) ranges from about 2% to as high as about 40%. The accuracy of the non-invasive prenatal test is typically higher When the fraction of fetal DNA in the maternal plasma is higher. A big challenge for cfDNA based NIPT is that the fetal fraction has a high variance4even at a ?xed gestational age the fetal fraction can range by more than an order of magnitude. Samples With high fetal fraction, for example above 10% fetal DNA, typically result in accurate results. HoWever, samples With a loW fetal fraction, for example beloW 5% fetal DNA typically result in very poorly accurate results or a high rate of “no calls” (samples for Which a result is not reported due to lack of conclusive data.) Meth ods that are able to increase the fetal fraction Will tend to increase the accuracy of any prenatal tests that rely on mea suring fetal cfDNA. One Way to conceptualiZe this is to think of the fetal DNA as the signal, and the maternal DNA as the noise. The more signal present, the easier it is to decipher the signal. [