The screech frequency of axially symmetric choked jets falls steadily with decreasing pressure ratio, with several frequency jumps, some up, some down [A. Powell, Proc. Phys. Soc. London Ser. B 66, 1039‐1056 (1953)]. Davies and Oldfield's Lissajous figures [Acustica 12, 267–277 (1962)] showed that the corresponding jet oscillation modes are of various types. Schlieren photography and digitally processed acoustic pressure signals are now used. Unambiguously, the first two modes, a1 and a2, are axially symmetric (varicose, like ring vortices); the next, b, is asymmetric in an arbitrary plane (sinuous); c is helical, rotating in either sense, stable once started, while d is sinuous again, connected to c by hysterectic jumps. However, tone d is weakly but smoothly connected to b, so d appears to be an extension of b. Moreover, the dominant c tone extends weakly to overlap where b and d dominate, and a suspected weak a2(?) overlaps where b, c, and d dominate. Further, both a1 and b exist weakly where a2 dominates. Evidently jumps occur not necessarily at changes in the mode as previously thought, but when there is a change in which one dominates.