A word group among the Uralic etymological comparative material with remarkably messy sound correspondences is that for ‘swan’. The following candidates for inclusion are usually identified (all with the same meaning):
- Samic *ńukčë (> Southern njoktje, Northern njukča, Kildin нюххч, etc.)
- Finnic *jouccën (> Estonian jõudsin, Finnish joutsen, Veps ďoutšin, etc.)
- Mordvinic *lokśəj (> Erzya локсей, Moksha локсти)
- Mari *jükćə (> Hill йӱкшӹ, Meadow йӱксӧ)
- Permic *juśk- (> Udmurt, Komi юсь; Komi stem юськ-)
- 18th century Mansi joschwoi
Two different reconstructions are found in the usual general-purpose sources: *joŋkće (UEW) and *ńokśi (HPUL). Neither of these can be called satisfactory, I think. In the following I’ll go over some issues that can probably be resolved, or at least worked around to some extent:
UEW’s reconstruction foremost suffers from the problem that CCC clusters are generally poorly supported for Proto-Uralic. Moreover, this particular case has only been supposed in order to explain the correspondence between an *u-diphthong in Finnic vs. syllable-final *k elsewhere (regularly metathesized in Permic). The cluster would thus have been then simplified to *ŋć in pre-Finnic, *kć elsewhere. This is a very ad hoc way of reconciling irregular reflexes — it would make just about as much sense e.g. to claim an onset cluster *nj or *lj, to account for the irregular *ń- in Samic or *l- in Mordvinic.
Earlier I had suspected that simply *joŋćə could be made work, but getting from a nasal to *k elsewhere appears too troublesome. It is true that Samic clearly has similar denasalization in *joŋsə >> *jōksë ‘bow’ (possibly indeed mediated by epenthesis to *ŋks), but Mari *jåŋež and Mordvinic *joŋs do not support supposing this. Also, while there is some curious resemblance here with Proto-Indo-European *ǵʰans- ‘goose’, it’s probably too little to be worth pursuing, in the end. The semantic difference aside, *ǵ⁽ʰ⁾ ~ *j would most likely indicate a loanword from IE to Uralic, while *ŋć ~ *ns looks like it could only work in some kind of an Indo-Uralic framework.
I now favor a different explanation: reconstructing the cluster *xć.
Distinguishing Proto-Uralic *x and *k is challenging. They have identical direct reflexation in all branches other than Finnic (where between vowels *-x- > ∅, but *-k- > *-k-) and Mordvinic (where between back vowels *-x- > *-j-, but *-k- > *-v-). This being the case, I consider it likely that some portion of the unusually frequent *-Ck- and *-kC- consonant clusters in Proto-Uralic  might be actually so far unidentified instances of *-Cx- or *-xC-. This is all the more likely these days, now that the old reconstruction by Janhunen of syllable-final *x for words showing a Finnish long vowel is no longer current (so e.g. PF *meeli ‘mind’ < *mälə and not **mäxlə; PF *koole- ‘to die’ < *kalə- and not **kaxlə-).
We also happen to already know that in Finnic, the regular outcome of syllable-final *x is vocalization to *u ~ *ü, as is shown by the two Finnic verb roots *souta- ‘to row’, *nouta- ‘to fetch’, which derive from PU *suxə- ‘to row’, *ńoxə- ‘to pursue’ (with the common verbal suffix *-ta- appended for no clear reason).  So the expected reflex of *-xć- in Finnic will be indeed *-uc-.
Nothing on the other hand seems to majorly contradict the idea that elsewhere in Uralic, syllable-final *x has again generally merged with *k. *souta- does has a Samic formal equivalent: *suvtē- ‘to transport by boat’, but perhaps this is an old Finnic loanword (vs. the bare root in *sukë- ‘to row’ being the native reflex)?
This reconstruction also allows better odds that the Mansi word indeed belongs here. László Honti has commented  that the loss of the entire cluster *ŋk seems unlikely. The development *x > ∅ would surely be less troubling though, especially syllable-finally in a compound word. (The second element is clearly *wuj ‘animal’.) He also notes that joschwoi (*jōšwoj?) seems cognate with modern Northern Mansi jūswoj ‘eagle sp.’, and that the earlier meaning of the word might not even have been ‘swan’ as much as ‘large bird’. But if these meanings are connected, I could just as well imagine a development route ‘swan’ > ‘large bird’ > ‘eagle’.
— Some other examples *xC clusters can perhaps also be located. Further research will be necessary, but one case that looks promising to me is Samic *piktē- ‘to heat’, which seems analyzable as a derivative < *pix-tä-, from the same root *pixə- ‘to cook’ (traditionally reconstructed as *peje- (UEW) or *pexi- (HPUL)) as Mordvinic *pijə-, Hungarian fő, Samoyedic *pi-.  Another possible case is ‘rope’: Mordvinic *piks, Khanty *püüɣəL, older Hungarian fiu < *pexsə. In both cases the vocalism in Samic (*i > *i and not > *ë) and Mordvinic (*i, *e > *i and not > *e) appears to suggest that *k < earlier *x. The same argument applies also to PS *u in ‘swan’.
Turning to vocalism, although earlier PU *o has been generally presumed in the 1st syllable, to me this seems based more on belief in the conservativeness of Finnic than in actual comparative considerations. In particular the correspondence between Samic *u, Finnic *o and Mari *ü appears fairly irregular. A lowering *u > *o before *x has sometimes been proposed for Finnic, mainly in ‘to row’ (cf. above); and it could be assumed here as well. This approach however does not work for Mari. In UEW, *ü is instead attributed to irregular “fronting influence” of the word-initial *j… but since the regular Mari reflex of *u is the “reduced-series” *ŭ (> Meadow Mari /u/, Hill Mari /ɤ/), then if starting from something like *juxćə, we’d surely expect the result of fronting to be its front counterpart *ü̆ (> Meadow Mari /y/, Hill Mari /ə/).
A more promising solution seems to be provided by some closely related soundlaws recently proposed by Mikhail Zhivlov: PU *ë-ə before a velar consonant > pre-Samic/Mordvinic *u, Finnic *o, which would turn up in some other widespread Uralic words as well, perhaps most prominently ‘to drink’ (S. *jukë-, F. *joo-, versus Mari *jüä-, Hungarian ív-).  Mari *ü and Permic *u will then turn out to be simply the usual reflexes of *ë.
I thus arrive at the improoved reconstruction *jëxćə.
(Update 2018-03-23: after some review of the development of *ë in Mari I am now rather more skeptical of reconstructing PU *ë in this word.)
All sorts of other issues still remain:
- For the initial consonant, *j of course seems like the safest bet. Unlike Sammallahti, I see no reason to privilege Samic *ń-. There are no parallels for its lenition to *j- in the other Uralic languages. If anything, I wonder if the nasal can have an onomatopoetic function here? though swan calls do not strike me as especially nasal at all. Mordvinic *l- is a complete mystery too. I would suggest contamination from *lunta ‘goose’, but this word has not survived in the branch.
- Mordvinic *o could indeed reflect earlier *u, but my tangentially covered etymology/reconstruction above of *pijə- ‘to cook’ < PU *pixə- assumes *x to block the lowering of close vowels, same as it does in Samic. But could *x > *k syllable-finally have already occurred in Mo. before this?
- *oo in Mansi, if it belongs here, probably cannot be derived from *ë (and is also at best a rare reflex of *o as well).
- Similarly, if sch is /š/, this cannot be derived from *ć. It’s attested as a “sporadic” reflex of *ś though.
- The geminate affricate in Finnic is curious. Other cases of apparent *ć > *cc exist as well, e.g. PU *wäńćə > PF *väicci > Fi. veitsi ‘knife’; PF *icek > Fi. itse ‘self’ (but Es. ise). This is also in contrast to secondary affricates due to the Proto-Finnic sound change *ti > *ci coming out consistently short (and being then further reduced to plain s.)
- The Mari dialects run the full gamut with their sibilants, showing varyingly š, s, ś, ć, and it’s not clear to me what is going on. The contrast between PU *ś and *ć is at least as difficult to reconstruct as that between *x and *k, though less due to coinciding reflexes, and more due to most subgroups being highly inconsistent on if they show affricates or fricatives (the only relatively clean cases are Samic and Samoyedic). Subgroup-internal snafus like this do not help.
- I suspect *kć > *kś to be regular for Mordvinic, but who knows. There are very few examples of *Cć to begin with, and the most reliable-looking case (*ńëkćəm ‘gills’) has no Mordvinic reflex.
 For some discussion, see e.g. Mikko Korhonen (1986), On the reconstruction of Proto-Uralic and Proto-Finno-Ugrian consonant clusters, Suomalais-Ugrilaisen Seuran Aikakauskirja 80. Korhonen characterizes the issue as one of a lack of consonant clusters of the shape dental + dental (and indeed, *lt and *rt seem to have been absent from the PU lexicon) — but it is also the case that clusters with a velar member, e.g. *ŋk, *lk, *ks, appear to be much more numerous and better-established than clusters with a labial member, e.g. *mp, *lp, *ps.
 This result is, paradoxically enough, also due to Janhunen. He accomplishes this by assuming an early vocalization in words of the ‘mind’, ‘to die’ type, and a late vocalization in ‘to row’, ‘to fetch’. See Juha Janhunen (2007), The primary laryngeal in Uralic and beyond, Suomalais-Ugrilaisen Seuran Toimituksia 253: 203–227.
 László Honti (1985), Etimológiai adalékok, Nyelvtudományi Közlemények 87/2: 444.
 Komi pu- ‘to cook’ will have to be discarded from this etymology however, it seems. Not that this is regular either way: while *e normally yields close back /u/ in Udmurt and Jazva Komi, almost all clear cases show /o/ in mainline (Zyrian / Permyak) dialects of Komi, a correspondence that is normally also attributed to a different Proto-Permic vowel from those showing /u/-across-the-line. I would also separate Mansi *pääj- ‘to cook’, though this word will not have to end up as an etymological orphan: it seems instead derivable from the “heat-and-light” root *päjə, whose potential reflexes include e.g. Samic *peajvē ‘day, sun’ and *peajō- ‘to shine’, Finnic *päjwä ‘day’, Komi bi ‘fire’, Hungarian fehér ‘white’, Khanty *pääj ‘thunder’, Samoyedic *päjwä ‘heat’ (some of these more, some less probable — the semantics in particular would require review).
 Mikhail Zhivlov (2014), Studies in Uralic vocalism III, Journal of Language Relationship 12: 115–116. I am actually not entirely sold on this idea yet, since the changes seem to lack phonetic motivation, and are based on a very small set of data. But for now it seems at least worth keeping in mind.