Current road roughness indexes are limited to reflecting the unwanted rotational vibration of vehicles. This study focused on the relationship between the international roughness index (IRI) and rotational vibration around the longitudinal axis (pitch) and horizontal axis (roll) of the vehicle body. Sinusoidal wave input of different wavelengths and phase shifts between the left and right wheel tracks were used as excitation of a full-car model. Marked pitch and roll vehicle vibration were observed at shorter wavelengths (<1 m) and lower speeds (<50 km/h) of harmonic excitation. The IRI was limited to predicting the pitch and roll vibration of the full-car model at lower wavelengths, below 1 m. A simple alternative solution based on the IRI model was proposed as a robust, sensitive tool to detect unwanted rotational vibration of a vehicle. The proposal was based on the IRI approach using an alternative IRI model speed of 30 km/h, instead of the standard 80 km/h. The IRI for 30 km/h was several times more sensitive to pitch and roll vibration in the wavelength band up to 1.5 m than the IRI for 80 km/h. The new approach is recommended as an additional roughness index for monitoring roads with an allowable speed of up to 60 km/h.