Also known as Condorcet-Hare or Condorcet-RCV methods. These are Condorcet methods that use IRV/RCV-related methods to resolve cycles. See Single transferable vote#Ways of dealing with equal rankings for information on dealing with equal rankings in these methods.
The complexity of these methods, from most simple to least, is generally BTR-IRV>Benham's>Woodall's>Smith//IRV>Tideman's Alternative methods. However, the difficulty of counting each method is almost the exact opposite order (except that BTR-IRV is relatively somewhat easy to count); this is because the more complex methods tend to eliminate candidates by looking at both their pairwise matchups and their 1st choice totals, whereas the simpler methods only eliminate candidates based on the latter, thus requiring more eliminations.
Condorcet-IRV methods are mostly immune to the DH3 scenario; this is because they eliminate the Dark Horse candidate for having little 1st choice support. The Condorcet-IRV methods which start by eliminating everyone outside the Smith set also tend to be much less susceptible to ties than regular IRV, since the Smith set is unlikely to have more than 3 candidates, and thus only one or a few eliminations must be done. See https://rangevoting.org/IRVamp.html for an example of near-ties affecting IRV.Condorcet-IRV methods, being Condorcet methods, all fail later-no-harm, whereas IRV doesn't. Example:
49 A>BB is the Condorcet winner, and would win in any Condorcet-IRV method. But if the 49 A>B voters didn't rank B, then (all?) Condorcet-IRV methods elect A. Notice that there is a spoiler effect here, as if C hadn't run, then B would've still won, an improvement from the perspective of the 48 C>B voters.
3 B48 C>B
Most Condorcet-IRV methods pass some form of dominant mutual third-related property. This ensures that they are strategyproof when there is a dominant mutual third set in the election.