Yet another follow-up to my earlier observation that the dinosaur to bird theory has many state transitions, lengthy ghost lineages and numerous exaptations.
You responded:
"Cladistic analysis that include modern birds and mesozoic theropods include big transitions, because of the big chronological gap. But analyses that include a good selection of ancient and modern birds as well as anceint theropods have nice, clean transitions of only a few characters each. The difficulty is drawing a line at any point and saying "the animals more derived that this, we will count as birds". There's no obvious place on the tree to do this, precisely because the transition is so smooth".

Please consider this study which I suggest shows that the transition is far from smooth:
An Archaeopteryx-like theropod from China and the origin of Avialae (2011)

If you look within the supplementary information (Section 7. Phylogenetic Analysis) you will see that Paraves has 51 unambiguous synapomorphies out of the 374 characteristics measured. Over 13% difference.
This means that Paraves is not "a smooth transition" but rather a large jump.
It is not correct to say that "there are nice, clean transitions of only a few characters each".

You will also notice another large jump at the step before that as well.

I imagine the issue here is taxon selection in the specific analysis you mention. I'll leave it to a theropod specialist to comment further.