Rating collateralized debt obligations (CDOs), ie, tranched pools of credit risk exposures, not only requires attributing a probability of default to each obligor within the portfolio. It also involves assumptions concerning recoveries and correlated defaults of pool assets, thus combining credit risk assessments of individual collateral assets with estimates about default correlations and other modeling assumptions. We explain one of the most well-known models for rating CDOs, the so-called binomial expansion technique (BET). Using simple, illustrative examples, we compare this approach with an alternative methodology based on Monte Carlo simulation. We then highlight the potential importance of correlation assumptions for the ratings of senior CDO tranches and explore what differences in methodologies across rating agencies may mean for senior tranche rating outcomes. Finally, we talk about potential implications of certain model assumptions for ratings accuracy, that is the “model risk” taken by investors, and discuss whether and under what conditions methodological differences may generate incentives for issuers to strategically select rating agencies to get particular CDO structures rated.