Recent advancements in DNA sequencing by end-labeled free-solution electrophoresis (ELFSE) show the promise of this novel technique which overcomes the need for a gel by using a label (or drag-tag) to render the free solution mobility of the DNA size-dependent. It is the attachment of an uncharged drag-tag molecule of a set size to various lengths of DNA in the sample that selectively slows down smaller DNA chains which have less force to pull the drag-tag than larger DNA. So far, only globally random coil conformations have been associated with ELFSE, i.e., the DNA and the label together form a single, undeformed hydrodynamic unit. This paper investigates the conditions under which the DNA and label will segregate into two hydrodynamically distinct units, based on a theoretical approach developed for the electrophoresis of polyampholytes. Optimal experimental conditions tailored to the available label sizes and voltages are predicted along with insight into ideal label architecture.