The Bundled Payments for Care Improvement initiative Advanced Model (BPCI Advanced) is a voluntary Medicare bundled payment model in which hospitals may participate with third-party conveners-private consulting firms that share in the financial risk built into the program. We found that nonteaching and for-profit status was associated with a higher probability of hospital partnership with third-party conveners in BPCI Advanced. Among hospitals participating in at least one inpatient clinical episode, hospitals that partnered with third-party conveners were more likely to select episodes with higher target prices: A $1,000 increase in episode target price was associated with a 1.66-percentage-point increase in the probability of episode participation in BPCI Advanced compared with a 0.72-percentage-point increase for participating hospitals without third-party conveners. Hospitals with third-party conveners also were more likely than those without them to select inpatient clinical episodes with greater opportunities to reduce spending on postacute care and readmissions. These findings have important implications for understanding the role of private consulting firms in the program and for planning potential program modifications in the future.