Chipless tag systems composed of multimode stepped impedance resonators (SIRs) and a reader based on near-field electromagnetic coupling have been reported. This resonator structure has advantages including a simple design due to its symmetrical structure and good discrimination accuracy because many higher-order mode resonant frequencies can be used for identification of codes. However, in addition to the disadvantage of long resonator length, the frequency response in the tag system becomes unstable due to deterioration of the isolation between the probes because the same probe structure is used for the excitor and detector. In this paper, we propose two methods to solve these problems. One is to adopt an asymmetrical SIR structure with a short-circuited end and open-circuited end, which reduces the resonator length by half while allowing the same number of codes to be generated. The other is to improve isolation between probes by applying different magnetic field and electric field structures to the two probes for excitation and detection. We also examined assignment and identification conditions and clarified that the available number of codes for a unit tag can be more than 15 bits. It becomes clear that a 75-bit chipless tag on a credit card-sized (55×86mm) printed circuit board can be designed by integrating five unit tags.