A method for detecting the presence or absence of fetal nucleic acid in a substantially cell-free biological composition or a cell-free biological composition, which comprises: (a) contacting cell-free nucleic acid from the biological composition with a solid phase under association conditions, wherein: (i) the nucleic acid of the biological composition comprises relatively short nucleic acid and relatively long nucleic acid, (ii) the relatively short nucleic acid may comprise fetal nucleic acid, (iii) the relatively short nucleic acid is 300 base pairs or less, (iv) the relatively long nucleic acid is larger than 300 base pairs, and (v) the association conditions include a C1-C6 alkyl alcohol and do not include a volume exclusion agent, whereby the relatively short nucleic acid and the relatively long nucleic acid are associated with the solid phase; (b) introducing the solid phase after (a) to dissociation conditions that comprise a volume exclusion agent and a salt, wherein: (i) the salt is an ionic salt and not a chaotropic salt, and (ii) the relatively short nucleic acid preferentially dissociates from the solid phase under the dissociation conditions as compared to the relatively long nucleic acid, thereby yielding dissociated nucleic acid; (c) separating the dissociated nucleic acid from the solid phase, whereby the fetal nucleic acid, when present, is enriched in the dissociated nucleic acid relative to in the cell-free nucleic acid from the biological composition; and (d) detecting the presence or absence of fetal nucleic acid in the biological composition, wherein "substantially cell-free" refers to up to 50 cells per milliliter. (a) contacting cell-free nucleic acid from the biological composition with a solid phase under association conditions, wherein: (i) the nucleic acid of the biological composition comprises relatively short nucleic acid and relatively long nucleic acid, (ii) the relatively short nucleic acid may comprise fetal nucleic acid, (iii) the relatively short nucleic acid is 300 base pairs or less, (iv) the relatively long nucleic acid is larger than 300 base pairs, and (v) the association conditions include a C1-C6 alkyl alcohol and do not include a volume exclusion agent, whereby the relatively short nucleic acid and the relatively long nucleic acid are associated with the solid phase; (i) the nucleic acid of the biological composition comprises relatively short nucleic acid and relatively long nucleic acid, (ii) the relatively short nucleic acid may comprise fetal nucleic acid, (iii) the relatively short nucleic acid is 300 base pairs or less, (iv) the relatively long nucleic acid is larger than 300 base pairs, and (v) the association conditions include a C1-C6 alkyl alcohol and do not include a volume exclusion agent, whereby the relatively short nucleic acid and the relatively long nucleic acid are associated with the solid phase; (b) introducing the solid phase after (a) to dissociation conditions that comprise a volume exclusion agent and a salt, wherein: (i) the salt is an ionic salt and not a chaotropic salt, and (ii) the relatively short nucleic acid preferentially dissociates from the solid phase under the dissociation conditions as compared to the relatively long nucleic acid, thereby yielding dissociated nucleic acid; (i) the salt is an ionic salt and not a chaotropic salt, and (ii) the relatively short nucleic acid preferentially dissociates from the solid phase under the dissociation conditions as compared to the relatively long nucleic acid, thereby yielding dissociated nucleic acid; (c) separating the dissociated nucleic acid from the solid phase, whereby the fetal nucleic acid, when present, is enriched in the dissociated nucleic acid relative to in the cell-free nucleic acid from the biological composition; and (d) detecting the presence or absence of fetal nucleic acid in the biological composition,