Selection of affinity ligands for protein targets from oligonucleotide libraries currently involves multiple rounds of alternating steps of partitioning of protein-bound oligonucleotides (binders) from protein-unbound oligonucleotides (nonbinders). We have recently introduced ideal-filter capillary electrophoresis (IFCE) for binder selection in a single step of partitioning. In IFCE, protein-binder complexes and nonbinders move inside the capillary in the opposite directions, and the efficiency of their partitioning reaches 10(9), i.e., only one of a billion molecules of nonbinders leaks through IFCE while all binders pass through. The condition of IFCE can be satisfied when the magnitude of the mobility of EOF is smaller than that of the protein-binder complexes and larger than that of nonbinders. The efficiency of partitioning in IFCE is 10 million times higher than those of solid-phase-based methods of partitioning typically used in selection of affinity ligands for protein targets from oligonucleotide libraries. Here, we provide additional details on our justification for IFCE development. We elaborate on electrophoretic aspects of the method and define the theoretical range of EOF mobilities that support IFCE. Based on these theoretical results, we identify an experimental range of background electrolyte's ionic strength that supports IFCE. We also extend our interpretation of the results and discuss in-depth IFCE's prospective in practical applications and fundamental studies.