This paper presents a framework in which many structural credit risk models can be made hybrid by randomizing the default trigger while keeping the capital structure intact. This produces random recovery rates negatively correlated with the default probability. The approach is implemented on a firm-by-firm basis, using maximum likelihood and the unscented Kalman filter on each of the 225 companies of the CDX North American Investment Grade and High Yield indexes using weekly credit default swap data from December 2007 to January 2012. The proposed framework has been benchmarked against two intensity-based models and a structural model. The in-sample and out-of sample measures indicate that, overall, the hybrid framework dominates the other three models. Adding the surprise element and the time-varying distribution of recovery rates has a large impact on credit spreads as they modify both the level and the shape of the curves.