This paper deals with a unified way for calculating vortex-induced vibrations (Aeolian vibrations in transmission line parlance) of undamped single overhead conductors. The main objective of the paper is to identify reduced parameters which would unify the predicted vibration response to the largest possible extent. This is actually done by means of a simple mathematical transformation resulting, for a given terrain (associated to a given wind turbulence intensity), into a single, unified response curve that is applicable to any single multi-layered aluminium conductor. In order to further validate the above process, the predicted, unified response curve is compared with measured response curves drawn from tests run on a full-scale test line using several aluminium-conductor-steel-reinforced (ACSR), all-alloy-aluminium-conductor (AAAC) and aluminium-conductor-alloy-reinforced (ACAR) conductors strung at different tensions. On account of the expected scatter in the results from such field tests, the agreement is shown to be good. The final results are expressed by means of only four different curves pertaining to four different terrain characteristics. These curves may then be used to assess the vibration response of any undamped single, multi-layer aluminium conductor of any diameter, strung at any practical tension.