Abstract Composition and spectra of Galactic cosmic rays (CRs) are vital for studies of high-energy processes in a variety of environments and on different scales, for interpretation of γ -ray and microwave observations, for disentangling possible signatures of new phenomena, and for understanding of our local Galactic neighborhood. Since its launch, AMS-02 has delivered outstanding-quality measurements of the spectra of , , and nuclei: 1 H– 8 O, 10 Ne, 12 Mg, 14 Si. These measurements resulted in a number of breakthroughs; however, spectra of heavier nuclei and especially low-abundance nuclei are not expected until later in the mission. Meanwhile, a comparison of published AMS-02 results with earlier data from HEAO-3-C2 indicates that HEAO-3-C2 data may be affected by undocumented systematic errors. Utilizing such data to compensate for the lack of AMS-02 measurements could result in significant errors. In this paper we show that a fraction of HEAO-3-C2 data match available AMS-02 measurements quite well and can be used together with Voyager 1 and ACE-CRIS data to make predictions for the local interstellar spectra (LIS) of nuclei that are not yet released by AMS-02. We are also updating our already-published LIS to provide a complete set from 1 H– 28 Ni in the energy range from 1 MeV nucleon −1 to ∼100–500 TeV nucleon −1 , thus covering 8–9 orders of magnitude in energy. Our calculations employ the G al P rop –H el M od framework, which has proved to be a reliable tool in deriving the LIS of CR , e − , and nuclei 1 H– 8 O.