Above their 'percolation threshold', intrinsically conducting polymer (ICP) based composites exhibit an increase or decrease in conductivity with strain. However, in this study we report an increase in conductivity and an associated insulator-to-conductor transition observed in certain conducting polymer composites below their percolation threshold under uniaxial tensile strain, thereby shifting the percolation to lower volume fractions. The 'auxetic behaviour' possible in certain types of 'hierarchical' microstructures is shown to be responsible for such changes in the polyaniline (PANI) composites studied. Using percolation models, the size and shape of the 'conducting units' that contribute to the percolation and its changes with strain were predicted. These conducting units are secondary and tertiary 'hierarchical structures' formed by the agglomeration of primary units of nano-rods (10 nm). An increase in the aspect ratio of these 'conducting units' is necessary for lowering the percolation threshold, which is possible in tertiary rod-like assemblies of PANI and not in secondary rod-like or platelet-like hierarchical structures. 'Auxetic behaviour' or a negative Poisson's ratio results in the expansion of the agglomerates and increase in the aspect ratio. This demonstrates the possibility of 'auxetic behaviour' contributing to changes in conductivity, which has not been reported before and could be used for novel applications. © 2017 the Owner Societies.