MicroRNA (miRNA) biogenesis is initiated upon cleavage of a primary miRNA (pri-miRNA) hairpin by the Microprocessor (MP), composed of the Drosha RNase III enzyme and its partner DGCR8. Multiple pri-miRNA sequence motifs affect MP recognition, fidelity, and efficiency. Here, we performed cryoelectron microscopy (cryo-EM) and biochemical studies of several let-7 family pri-miRNAs in complex with human MP. We show that MP has the structural plasticity to accommodate a range of pri-miRNAs. These structures revealed key features of the 5' UG sequence motif, more comprehensively represented as the "flipped U with paired N" (fUN) motif. Our analysis explains how cleavage of class-II pri-let-7 members harboring a bulged nucleotide generates a non-canonical precursor with a 1-nt 3' overhang. Finally, the MP-SRSF3-pri-let-7f1 structure reveals how SRSF3 contributes to MP fidelity by interacting with the CNNC motif and Drosha's Piwi/Argonaute/Zwille (PAZ)-like domain. Overall, this study sheds light on the mechanisms for flexible recognition, accurate cleavage, and regulated processing of different pri-miRNAs by MP.