This paper analyses the allocation of R&D investments within rare diseases and identifies the characteristics of rare diseases that appear to lead R&D resources. Rare diseases affect less than 1 in 2,000 citizens. With over 7,000 recognized rare diseases and 350 million people affected worldwide, rare diseases are not so rare when considered collectively. Rare diseases are generally underserved by drug development because pharmaceutical industries consider R&D investments in rare diseases too costly and risky in comparison with the low expected returns due to the small population involved. We use data on rare diseases research from Orphanet along with academic publications per rare disease from bibliographic databases. We test the existence of inequalities in R&D investments within rare diseases and identify the disease characteristics that appear to lead R&D investments using dominance tools and bilateral tests. We show that rare diseases in children and with a smaller prevalence, such as ultra-rare diseases, are underserved by R&D. R&D investments appear to be concentrated in more profitable research areas with potentially larger sample size and adult population.