For many surgical procedures, apparent volume–outcome relationships may reflect differences in patient risk-profiles as well as quality of care. As some important patient profile differences may be unobserved, we use fixed effects (FE) regression to estimate the relationship between operative mortality and surgeon and hospital volumes, and compare this method with the more commonly used random effects (RE) regression approach. The 1998 and 1999 Medicare Inpatient and Denominator files for Medicare Fee for Service enrollees aged 65–99. Operative mortality rates are estimated for different surgeon and hospital volume tertiles (high, medium, low) using FE and RE regression methods, adjusted for patient demographics and morbidities. The data were collected by the Centers for Medicare and Medicaid Services (CMS). FE regression estimates that lowest volume tertile hospitals have 1.4 and lowest volume tertile surgeons have 1.6 additional operative deaths (for every 100 CABG surgeries) compared to their highest volume tertile counterparts. The corresponding RE estimates are 0.5 and 1.4 respectively. The substantially higher FE hospital volume effect compared to RE indicates the presence of unobserved “protective” characteristics in lower volume providers, including a less complicated patient profile. Lower hospital and surgeon volumes are associated with substantially higher excess operative mortality from CABG surgeries than previously estimated.