In this study, lattice physics calculations were carried out to evaluate the reactor physics characteristics of different advanced fuel lattices cooled with 7LiOH/NaOH or FLiBe and moderated externally by graphite and various types of metal hydroxides, such as 7LiOH, 7LiOD, Mg(OD)2, and ZrE(OD)4. The lithium in these compounds is enriched to 99.995 at. % 7Li/Li. Such lattice fuel concepts could be used in compact, thermal-spectrum, high-temperature (700°C) small modular reactors (SMRs). For an SMR with a bare core size of diameter = height = 163.3 cm, there are several lattice design concepts identified that could achieve modest power densities (up to 18 MW/m3) that are higher than those found typically in high-temperature gas cooled reactors (~ 2 to 10 MW/m3) [IAEA Technical Document 1382 (2019); Report PNR-131-20110914, Delft University, Netherlands (2011)], although lower than those found typically in SMRs based on light water reactor technology (for example, the NuScale SMR has a volumetric power density of ~47 MW/m3) [Proc. PBNC 2018, p. 270 (2018)]. In addition, there are lattice designs identified for the fixed core size that could achieve high fuel burnup (up to 126 MWd/kg), long core lifetimes (up to 24 years before refueling), very good fissile utilization (up to 640 MWd/kg-fissile), and very good relative uranium utilization (up to 44% of that achieved with a conventional pressure-tube heavy water reactor using natural uranium fuel). The best lattice concept found to maximize fuel burnup with 7LiOH/NaOH coolant was an 18-cm-pitch lattice with ZrE(OD)4 external moderator (126.5 MWd/kg). The best lattice concept for FLiBe coolant was a 16-cm-pitch lattice with 7LiOH external moderator (125.99 MWd/kg). Although it is recognized that there are numerous and challenging technical issues to be resolved, particularly with corrosion and materials science, the potential use of hydroxides as coolants and/or external moderators could lead to very important performance improvements for very small and compact SMRs.