Observational evidence supports the recent analytical prediction that tornado intensities are exponentially distributed over peak wind speed squared (v2), or equivalently, Rayleigh-distributed over v. For large USA data samples, exponential tails are found in the tornado intensity distributions over v2 from about F2 intensity on. Similar results follow for smaller worldwide data samples. For the 1990s data from the USA and Oklahoma, deviations from the Rayleigh distribution for weak tornadoes can be explained by the emergence of a separate, likely non-mesocyclonic tornado mode. These bimodal datasets can be modeled by superposition of two Rayleigh distributions. The change in modal dominance occurs at about the F2 threshold (v ≈ 50 m s-1). In France, likely mainly the mesocyclonic tornado mode has been recorded, while in the UK, only a non-mesocyclonic mode seems to be present.