The nuclear cap-binding complex (CBC) stimulates multiple steps in several RNA maturation pathways, but how it functions in humans is incompletely understood. For small, capped RNAs such as pre-snRNAs, the CBC recruits PHAX. Here, we identify the CBCAP complex, composed of CBC, ARS2 and PHAX, and show that both CBCAP and CBC-ARS2 complexes can be reconstituted from recombinant proteins. ARS2 stimulates PHAX binding to the CBC and snRNA 3'-end processing, thereby coupling maturation with export. In vivo, CBC and ARS2 bind similar capped noncoding and coding RNAs and stimulate their 3'-end processing. The strongest effects are for cap-proximal polyadenylation sites, and this favors premature transcription termination. ARS2 functions partly through the mRNA 3'-end cleavage factor CLP1, which binds RNA Polymerase II through PCF11. ARS2 is thus a major CBC effector that stimulates functional and cryptic 3'-end processing sites.