Ray tracing hardware accelerators supporting multiple specifiers for controlling the traversal of a ray tracing acceleration data structure are disclosed. For example, traversal efficiency and complex ray tracing effects can be achieved by specifying traversals through such data structures using both programmable ray operations and explicit node masking. The explicit node masking utilizes dedicated fields in the ray and in nodes of the acceleration data structure to control traversals. Ray operations, however, are programmable per ray using opcodes and additional parameters to control traversals. Traversal efficiency is improved by enabling more aggressive culling of parts of the data structure based on the combination of explicit node masking and programmable ray operations. More complex ray tracing effects are enabled by providing for dynamic selection of nodes based on individual ray characteristics.