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Hot, compact, hydrogen-deficient pre-white dwarfs (pre-WDs) with effective temperatures of Teff > 70,000 K and a surface gravity of 5.0 < log g < 7.0 are rather rare objects despite recent and ongoing surveys. It is believed that they are the outcome of either single star evolution (late helium-shell flash or late helium-core flash) or binary star evolution (double WD merger). Their study is interesting because the surface elemental abundances reflect the physics of thermonuclear flashes and merger events. Spectroscopically they are divided in three different classes, namely PG1159, O(He), or He-sdO. We present a spectroscopic analysis of five such stars that turned out to have atmospheric parameters in the range Teff = 70,000-80,000 K and log g = 5.2-6.3. The three investigated He-sdOs have a relatively high hydrogen mass fraction (10%) that is unexplained by both single (He core flash) and binary evolution (He-WD merger) scenarios. The O(He) star JL9 is probably a binary helium-WD merger, but its hydrogen content (6%) is also at odds with merger models. We found that RL 104 is the 'coolest' (Teff = 80,000 K) member of the PG1159 class in a pre-WD stage. Its optical spectrum is remarkable because it exhibits C IV lines involving Rydberg states with principal quantum numbers up to n = 22. Its rather low mass (0.48 +0.03/-0.02 Msun) is difficult to reconcile with the common evolutionary scenario for PG1159 stars due to it being the outcome of a (very) late He-shell flash. The same mass-problem faces a merger model of a close He-sdO plus CO WD binary that predicts PG1159-like abundances. Perhaps RL 104 originates from a very late He-shell flash in a CO/He WD formed by a merger of two low-mass He-WDs., We thank Uli Heber for putting his CASPEC spectrum of JL 9 at our disposal and useful comments on an earlier version of the manuscript, and Max Pritzkuleit for his support of the HOTFUSS project. M.D. acknowledges funding by the Deutsche Forschungsgemeinschaft (DFG) through grant HE1356/71-1. R.R. has received funding from the postdoctoral fellowship programme Beatriu de Pinós, funded by the Secretary of Universities and Research (Government of Catalonia) and by the Horizon 2020 programme of research and innovation of the European Union under the Maria Skłodowska-Curie grant agreement No 801370. The TMAD tool (http://astro.uni-tuebingen.de/ ~TMAD) used for this paper was constructed as part of the activities of the German Astrophysical Virtual Observatory. Some of the data presented in this paper were obtained from the Mikulski Archive for Space Telescopes (MAST). This research has made use of NASA’s Astrophysics Data System and the SIMBAD database, operated at CDS, Strasbourg, France. This research has made use of the VizieR catalogue access tool, CDS, Strasbourg, France. This work has made use of data from the European Space Agency (ESA) mission Gaia., Peer Reviewed, Postprint (author's final draft)