Integrated memory circuits, key components in thousands of electronic and computer products, have been made using ferroelectric materials, which offer faster write cycles and lower power requirements than some other materials. However, the present inventors have recognized, for example, that conventional techniques for working with the polymers produce polymer layers with thickness variations that compromise performance and manufacturing yield. Accordingly, the present inventors devised unique methods and structures for polymer-based ferroelectric memories. One exemplary method entails forming an insulative layer on a substrate, forming two or more first conductive structures, with at least two of the first conductive structures separated by a gap, forming a gap-filling structure within the gap, and forming a polymer-based ferroelectric layer over the gap-filling structure and the first conductive structures. In some embodiments, the gap-filling structure is a polymer, a spin-on-glass, or a flow-fill oxide.