DWARF53 (D53) in rice (Oryza sativa) and its homologs in Arabidopsis (Arabidopsis thaliana), SUPPRESSOR OF MAX2-LIKE 6 (SMXL6), SMXL7 and SMXL8, are well established negative regulators of strigolactone signalling involved in shoot branching. Little is known of pea (Pisum sativum) homologs and whether D53 and related SMXLs are specific to strigolactone signalling pathways. Here, we identify two allelic pea mutants, dormant3 (dor3), and demonstrate through gene mapping and sequencing that DOR3 corresponds to a homolog of D53 and SMXL6/SMXL7, designated PsSMXL7. Phenotype analysis, gene expression, protein and hormone quantification assays were performed to determine the role of PsSMXL7 in bud outgrowth regulation and the role of PsSMXL7 and D53 in integrating strigolactone and cytokinin responses. Like D53 and related SMXLs, we show that PsSMXL7 is strigolactone degradable, and induces feedback upregulation of PsSMXL7 transcript. Here we reveal a system conserved in pea and rice, whereby CK also upregulates PsSMXL7/D53 transcripts, providing a clear mechanism for strigolactone and cytokinin cross-talk in the regulation of branching. Further deepening our understanding of the branching network in pea, we provide evidence that strigolactone acts via PsSMXL7 to modulate auxin content via PsAFB5, which itself regulates expression of strigolactone biosynthesis genes. We therefore show that PsSMXL7 is key to a triple hormone network involving an auxin-SL feedback mechanism and SL-CK crosstalk.