Ray-tracing algorithms can be used to render a virtual scene and to detect collisions between objects. Numerous ray-tracing algorithms have been proposed which use data structures optimized for specific cases (rigid objects, deformable objects, etc.). Some solutions try to optimize performance by combining several algorithms to use the most efficient algorithm for each ray. This paper presents a ray-traced collision detection pipeline that improves the performance on a graphicd processing unit (GPU) when several ray-tracing algorithms are used. When combining several ray-tracing algorithms on a GPU, a well-known drawback is thread divergence among work-groups that can cause loss of performance by causing idle threads. In this paper we avoid branch divergence by dividing the ray tracing into three steps with append buffers in between. We also show that prediction can be used to avoid unnecessary synchronizations between the CPU and GPU. Applied to a narrow-phase collision detection algorithm, results show an improvement of performance up to 2.7 times.