Noncoding RNAs (ncRNAs) play increasingly appreciated gene-regulatory roles. Here, we describe a regulatory network centered on four ncRNAs—a long ncRNA, a circular RNA, and two microRNAs—using gene editing in mice to probe the molecular consequences of disrupting key components of this network. The long ncRNA Cyrano uses an extensively paired site to miR-7 to trigger destruction of this microRNA. Cyrano-directed miR-7 degradation is much more effective than previously described examples of target-directed microRNA degradation, which come primarily from studies of artificial and viral RNAs. By reducing miR-7 levels, Cyrano prevents repression of miR-7–targeted mRNAs and enables accumulation of Cdr1as, a circular RNA known to regulate neuronal activity. Without Cyrano, excess miR-7 causes cytoplasmic destruction of Cdr1as in neurons, in part through enhanced slicing of Cdr1as by a second miRNA, miR-671. Thus, several types of ncRNAs can collaborate to establish a sophisticated regulatory network. Display omitted •A long noncoding RNA, a circular RNA, and two microRNAs form a regulatory network•The Cyrano long noncoding RNA directs potent, multiple-turnover destruction of miR-7•Unchecked miR-7 prevents accumulation of Cdr1as circular RNA in cytoplasm of neurons•miR-7 prevents this accumulation by enhancing the miR-671–directed slicing of Cdr1as Three different classes of noncoding RNA converge in a regulatory network whereby a long noncoding RNA represses a microRNA via target-directed microRNA degradation, which in turn enables the accumulation of a circular RNA in the mouse brain.