As is known, all geo-logarithmic indices enjoy the axiomatic properties of being proportional, commensurable and homogeneous, together with their cofactors (Martini 1992a). Geologarithmic price indices satisfying the axioms of monotonicity, basis reversibility and factor reversibility have been investigated by Marco Fattore (2010), who has shown that the superlative Fisher price index does not belong to this family of indices. In this article, we discuss geo-logarithmic price indices with reference to the Laspeyres-Paasche bounding test and we propose a modification of the considered index family that satisfies this test. We also modify the structure of geo-logarithmic indices by using an additional parameter and, following the economic approach, we list superlative price index formulas that are members of the considered price index family. We obtain a special subfamily that approximates superlative price indices and includes the Fisher, Walsh and Sato-Vartia price indices.