Aspects of this invention include a downhole tool (such as a steering tool) including first and second sensor sets for measuring substantially instantaneous drill string rotation rates. Each of the sensor sets includes at least one accelerometer disposed to measure cross-axial acceleration components. Embodiments of this invention advantageously enable gravitational and tool shock/vibration acceleration components to be cancelled out, thereby improving accuracy. Moreover, exemplary embodiments of this enable stick/slip conditions to be detected and accommodated.