The propagation of flat domains in soft ferromagnetic thin films with uniaxial anisotropy has been utilized in the past to implement low-cost nonvolatile shift register memories. However the low density of storage, the poor quality of the films, and the complexity of the structure have overwhelmed the inherent low material cost and simple manufacturing tooling. As a result, the devices have not been competitive. A novel, very simplified structure using chemically deposited soft and hard exchange-coupled thin films is described. Localized magnetostatic fields are created through rectangular wide regions of the propagation channels in order to permit the storage of very small domains and the control of the domain propagation when the shift conductors are current pulsed. Experimental work on a 104 kbits/cm2density register geometry is reported, and the improvements necessary to reach higher densities are discussed.