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For most printed-circuit transmission lines under most conditions of operation, the dominant mode on the line is purely bound at lower frequencies and becomes leaky at higher frequencies. We reported recently that by changing only the relative line dimensions (such as a strip width or a slot width) the bound and leaky modes can propagate simultaneously over a frequency range instead of being separate. More recently, we showed that this effect is general, occurring for many different line structures. The explanation for this initially unexpected behavior remained obscure, however. We report here the discovery of two new improper (or nonspectral) modal solutions, one real and one complex, which are in themselves completely nonphysical but whose evolution as a function of dimensional change serves to explain how the simultaneous propagation effect can occur. In this paper we present this evolution of behavior and also describe the unusual field properties of these two new improper modes.