Custom-made mandibular advancement devices (MADs) are reported as providing higher efficacy rates compared with thermoplastic heat-moulded MADs but at the price of higher costs and treatment delays. To determine whether a thermoplastic heat-moulded titratable MAD (ONIRIS; ONIRIS SAS, Rueil Malmaison, France) is non-inferior to a custom-made acrylic titratable MAD (TALI; ONIRIS SAS, Rueil Malmaison, France) for obstructive sleep apnoea (OSA). We conducted a multicentre, open, randomised controlled trial of patients with OSA refusing or not tolerating continuous positive airway pressure (CPAP). Participants were randomly assigned to a thermoplastic heat-moulded titratable device or a custom-made acrylic device for 2 months with stratification by centre and OSA severity. The non-inferiority primary outcome was a ≥50% reduction in apnoea-hypopnoea index (AHI) or achieving AHI <10 events/hour at 2 months. The non-inferiority margin was preset as a difference between groups of 20% for the primary outcome in the per-protocol analysis. Of 198 patients (mean age 51 SD, 12 years; 138 72.6% men; mean body mass index 26 SD, 2.7 kg/m ; mean AHI 26.6/hour SD, 10.4), 100 received TALI and 98 ONIRIS. In per-protocol analysis, the response rate was 51.7% in the TALI group versus 53.6% in the ONIRIS group (absolute difference 1.9%; 90% CI: 11% to 15%, within the non-inferiority margin). Effectiveness was the same for severity, symptoms, quality of life and blood pressure reduction. Patients in ONIRIS group reported more side effects and adherence was slightly better with TALI. In patients with OSA refusing or not tolerating CPAP, the thermoplastic heat-moulded titratable MAD was non-inferior in the short-term to the custom-made acrylic MAD. NCT02348970.