This paper presents slow-wave transmission lines based on non-periodic reactive loading. Specifically, the loading elements are stepped impedance shunt stubs (SISS). By sacrificing periodicity using SISS tuned to different frequencies, multiple transmission zeros above the pass band arise, and the rejection level and bandwidth of the stop band is improved as compared with those of periodic structures. Through a proper design, it is possible to achieve compact lines, simultaneously providing the required electrical length and characteristic impedance at the design frequency (dictated by specifications), and efficiently filtering the response at higher frequencies. These lines are applied to the design of a compact power splitter with filtering capability in this work. The length of the splitter, based on a 35.35 Ω impedance inverter, is reduced by a factor of roughly two. Moreover, harmonic suppression better than 20 dB up to the fourth harmonic is achieved.