C2H2 zinc fingers (C2H2-ZFs) are the most prevalent type of vertebrate DNA-binding domain, and typically appear in tandem arrays (ZFAs), with sequential C2H2-ZFs each contacting three (or more) sequential bases. C2H2-ZFs can be assembled in a modular fashion, providing one explanation for their remarkable evolutionary success. Given a set of modules with defined three-base specificities, modular assembly also presents a way to construct artificial proteins with specific DNA-binding preferences. However, a recent survey of a large number of three-finger ZFAs engineered by modular assembly reported high failure rates (∼70%), casting doubt on the generality of modular assembly. Here, we used protein-binding microarrays to analyze 28 ZFAs that failed in the aforementioned study. Most (17) preferred specific sequences, which in all but one case resembled the intended target sequence. Like natural ZFAs, the engineered ZFAs typically yielded degenerate motifs, binding dozens to hundreds of related individual sequences. Thus, the failure of these proteins in previous assays is not due to lack of sequence-specific DNA-binding activity. Our findings underscore the relevance of individual C2H2-ZF sequence specificities within tandem arrays, and support the general ability of modular assembly to produce ZFAs with sequence-specific DNA-binding activity.