A new class of distance-based molecular structure descriptors is put forward, aimed at eliminating a general shortcoming of the Wiener and Wiener-type indices, namely that the greatest contributions to their numerical values come from vertex pairs at greatest distance. The Q-indices, considered in this work, consist of contributions of vertex pairs that exponentially decrease with distance. It is shown that the Q-indices are equal to the Hosoya polynomial H(G, lambda), evaluated at a pertinently selected value of the variable lambda. (C) 2011 Elsevier B.V. All rights reserved.