Pre-mRNA processing steps are tightly coordinated with transcription in many organisms. To determine how co-transcriptional splicing is integrated with transcription elongation and 3' end formation in mammalian cells, we performed long-read sequencing of individual nascent RNAs and precision run-on sequencing (PRO-seq) during mouse erythropoiesis. Splicing was not accompanied by transcriptional pausing and was detected when RNA polymerase II (Pol II) was within 75-300 nucleotides of 3' splice sites (3'SSs), often during transcription of the downstream exon. Interestingly, several hundred introns displayed abundant splicing intermediates, suggesting that splicing delays can take place between the two catalytic steps. Overall, splicing efficiencies were correlated among introns within the same transcript, and intron retention was associated with inefficient 3' end cleavage. Remarkably, a thalassemia patient-derived mutation introducing a cryptic 3'SS improved both splicing and 3' end cleavage of individual β-globin transcripts, demonstrating functional coupling between the two co-transcriptional processes as a determinant of productive gene output.