Finding optimal parameters for acceleration structures for raytracing is key to improved performance. Previous research has shown that a speedup of over 10% of rendering time is possible. Some parameters are interdependent which complicates the process of finding an optimal configuration. It is hence interesting to find them efficiently. Autotuning is an automatic optimization scheme able to search for optimal configurations and has been applied successfully to kD-trees in the past, which we apply today on BVHs. The more parameters to optimize, the more difficult it is to find optimal solutions. In this article, we analyze in detail the behavior of the parameters and their impact on acceleration structure building and rendering time. We show the interdependence and context sensitivity (i.e., scene, viewpoint) of the parameters. Based on the use case, this allows to target only crucial parameters. Convergence speed towards an optimal configuration is essential. To find better parameters, the autotuner needs to build the acceleration structure over and over, changing parameters every time. We introduce a hybrid model-based prediction and online autotuning method to address this issue. The prediction model allows for both instantaneous near-optimal configurations when inputs are known or similar, and efficient search of the configuration space when inputs are completely new. Online autotuning outperforms configurations recommended in literature by up to 11% median. The prediction model achieves 95% of the maximum speedup of the autotuner while reducing 90% of its overhead. Thus, hybrid online autonuning enables always-on tuning in ray tracing.