Save every clone! In phage display, clones displaying ligands that hinder growth of phage are lost in amplification. Competition of slowly (S) and rapidly (R) growing phage is mitigated in monodisperse emulsions generated by a simple microfluidic device. Separating R and S in ca. 107 droplets maintains R/S ratio throughout amplification. Competition-free amplification of phage preserves ligands that are usually lost in phage display screen.