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Wave localization by flatband mechanisms underlies prominent moiré physics and relevant applications. While typically studied in periodic superlattices, the wave-confining capability of finite-size superlattices is important both fundamentally and practically. Here, we investigate wave localization in few-cell moiré superlattices through fine tuning of band offset, which is accomplished by jointly adjusting structural parameters of constitutive lattice. Remarkably, the quality factor Q, which reflects the capability of few-cell superlattices to localize wave, can reach quite high levels with appropriate band offset. Thus, superior wave localization is feasible in few-cell superlattices, indicated by the very high Q up to 10 4 − 10 5 for single-cell superlattices and extremely high Q up to > 10 7 for double-cell superlattices. Moreover, the Q patterns are distinct for different flatband resonances and different number of cells, while narrow high-Q (∼ 10 8 ) branches appear for the triple-cell superlattices. The narrow high-Q branches are hard to be reached in practice, since it requires stringent control on structural parameters. In this respect, the double-cell superlattices are promising for exploiting unconventional effects induced by wave localization, since it can achieve extremely high-Q (> 10 7 ) resonances within a sufficiently large tuning range. These results demonstrate the profound role of band-offset tuning in achieving strong wave localization in few-cell superlattices, which is useful for on-chip applications such as lasing, optical filters, and optical harmonic generation. [ABSTRACT FROM AUTHOR]