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In the course of the MUCHFUSS project we have recently discovered four radialvelocity (RV) variable, hot (Teff $\approx$ 80,000 - 110,000 K) post-asymptoticgiant branch (AGB) stars. Among them, we found the first known RV variableO(He) star, the only second known RV variable PG 1159 close binary candidate,as well as the first two naked (i.e., without planetary nebula (PN)) H-richpost-AGB stars of spectral type O(H) that show significant RV variations. Wepresent a non-LTE spectral analysis of these stars along with one furtherO(H)-type star whose RV variations were found to be not significant. We alsoreport the discovery of an far-infrared excess in the case of the PG 1159 star.None of the stars in our sample displays nebular emission lines, which can beexplained well in terms of a very late thermal pulse evolution in the case ofthe PG 1159 star. The "missing" PNe around the O(H)-type stars seem strange,since we find that several central stars of PNe have much longer post-AGBtimes. Besides the non-ejection of a PN, the occurrence of a late thermalpulse, or the re-accretion of the PN in the previous post-AGB evolution offerpossible explanations for those stars not harbouring a PN (anymore). In case ofthe O(He) star J0757 we speculate that it might have been previously part of acompact He transferring binary system. In this scenario, the mass transfer musthave stopped after a certain time, leaving behind a low mass close companionthat could be responsible for the extreme RV shift of 107.0 $\pm$ 22.0 km/smeasured within only 31 min.

RV variable, hot post-AGB stars from the MUCHFUSS project - Classification, atmospheric parameters, formation scenarios