Processing of histone pre-mRNA requires a single 3′ endonucleolytic cleavage guided by the U7 snRNP that binds downstream of the cleavage site. Following cleavage, the downstream cleavage product (DCP) is rapidly degraded in vitro by a nuclease that also depends on the U7 snRNP. Our previous studies demonstrated that the endonucleolytic cleavage is catalyzed by the cleavage/polyadenylation factor CPSF-73. Here, by using RNA substrates with different nucleotide modifications, we characterize the activity that degrades the DCP. We show that the degradation is blocked by a 2′-O-methyl nucleotide and occurs in the 5′-to-3′ direction. The U7-dependent 5′ exonuclease activity is processive and continues degrading the DCP substrate even after complete removal of the U7-binding site. Thus, U7 snRNP is required only to initiate the degradation. UV cross-linking studies demonstrate that the DCP and its 5′-truncated version specifically interact with CPSF-73, strongly suggesting that in vitro, the same protein is responsible for the endonucleolytic cleavage of histone pre-mRNA and the subsequent degradation of the DCP. By using various RNA substrates, we define important space requirements upstream and downstream of the cleavage site that dictate whether CPSF-73 functions as an endonuclease or a 5′ exonuclease. RNA interference experiments with HeLa cells indicate that degradation of the DCP does not depend on the Xrn2 5′ exonuclease, suggesting that CPSF-73 degrades the DCP both in vitro and in vivo.