The significance of varying the height and bandwidth of the group delay spectrum is hitherto unexplored in the spectral reconstruction of speech signals. In this paper, a family of variable height-bandwidth filters are designed to evaluate their performance in the reconstruction of speech. The design procedure for higher order group delay filters as a cascade of second order filters is first described. These higher order filters enable the synthesis of speech sounds by simultaneously varying the height and bandwidth of the group delay spectrum. The group delay filter response is corrected by removing zeros in close proximity to the unit circle which give rise to abrupt phase transitions at points of significant excitation. Experiments on spectral reconstruction and perception of speech using variable height bandwidth group delay filters are conducted to compute the optimal height and bandwidth of the group delay filter. The experimental results indicate that the optimal height bandwidth obtained from a family of variable height bandwidth group delay filters does indeed improve the spectral reconstruction and perception of speech sounds when compared to fixed height bandwidth group delay filters.