The cumulants of thermal variables are of general interest in physics due to their extensivity and their correspondence with susceptibilities. They become especially significant near critical points of phase transitions where they diverge along with the correlation length. Cumulant measurements have been used extensively within the field of heavy-ion physics, principally as tools in the search for a hypothetical QCD critical point along the transition between hadronic matter and QGP. The volume of individual heavy-ion collisions can be only partially constrained and, as a result, cumulant measurements are significantly biased by the limited volume resolution. We propose a class of moments called strongly intensive cumulants which can be accurately measured in the presence of unconstrained volume fluctuations. Additionally, they share the same direct relationship with susceptibilities as cumulants in many cases.