Excited states of the extremely neutron-deficient radon isotopes with N=111,113,115 have been studied for the first time in a series of in-beam experiments performed at the Accelerator Laboratory of the University of Jyväskylä. The reactions used were: Sn118(Kr82, 3n)Rn197, Sn120(Kr82, 3n)Rn199, Sm150(Cr52, 3n)Rn199, and Sn122(Kr82, 3n)Rn201. The γ rays emitted from excited states in the different isotopes were identified using the recoil-α-decay tagging technique. The estimated cross section for the production of 197Rnm was 7(3) nb, which is the lowest cross section reported so far for an in-beam study. The energies of the (17/2+) levels built on the isomeric (13/2+) states in Rn197,199,201 indicate a transition from an anharmonic vibrational structure toward a rotational structure at low spins for these nuclei. However, the transition is not as sharp as predicted by theory.