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The main, high-brightness neutron source for ESS is based on the low-dimensional moderator concept, and will serve the initial suite of neutron scattering instruments. In the HighNESS project several design options have been identified and investigated for a second source for ESS, intended to be complementary to the primary one. The emphasis of this project, completed in September 2023, was on the design of high-intensity sources, delivering Cold, Very Cold (VCN), and Ultra-Cold Neutrons (UCN). Remarkable results include: a cold moderator based on liquid deuterium capable of delivering an intensity close to a factor 10 greater than the ESS upper moderator; a VCN moderator based on solid deuterium at 5 K, surrounded by nanodiamond layers, delivering brightness above 40 Å an order of magnitude higher than a conventional cold moderator placed in the same location; and several design options for UCN sources based on the use of superfluid helium and solid deuterium. The use of these new sources would have a major impact on fundamental physics experiments and neutron scattering techniques. We investigate the possible impact that these concepts can have for compact sources, with particular emphasis on VCN.