It is well established that many mono-hydroxy alcohols show an extra relaxation process of the Debye type in addition to the signatures of primary and secondary structural relaxations, which is observed only in dielectric spectroscopy and related techniques. In order to gain further insight into the nature of this Debye peak, we study the linear and nonlinear dielectric behavior of a series of isomeric octyl alcohols and of mixtures of n-propanol with one of the octanols. These samples display systematic variations of the Debye peak intensity and concomitant changes in the Kirkwood correlation factor gK from 0.1 to 4, indicative of different equilibrium constants, K(c∕r), that characterize the populations of non-polar ring and polar open chain structures. For cases where K(c∕r) is not too far from unity, we find that a high electric field shifts K(c∕r) towards more chains, and that the accompanying change in the end-to-end vector of hydrogen-bond connected structures occurs on the Debye time scale. The results suggest that gK is correlated with the spectral separation of the Debye and primary structural peaks, as both features depend on steric hindrance of chain flexibility or bond rotation barriers and on average chain lengths. Based on the complex dynamics of supercooled mono-hydroxy alcohols with three relaxation peaks that cover many orders of magnitude in frequency, it is argued that a frequency dependent gK may be required for assessing the average orientational correlations within hydrogen-bonded structures correctly.