I went looking for more examples of dvandvas (for definition of dvandva see Warder pg 97) to see if they really are arranged in order of length by syllable count. Shortest element first, longest last and so on. In the section of Saddaniiti on pairs (and triads etc) that form neuter singulars there are 29 examples. I looked at all of them, and they confirm that the arrangement is in order of increasing syllable count. If anyone finds counterexamples or further interesting examples I'd be happy to see them.
Examples (from Saddaniiti, Suttamaala, Sutta 700)
cakkhu-sota.m (eye and ear)
mukha-naasika.m (mouth and nose)
chavi-ma.msa-lohita.m (skin, flesh and blood)
sa"nkha-pa.nava.m (conch and drum)
giita-vaadita.m (song and music)
daddarii-dindima.m (instrument and drum)
phaala-paacana.m (plowshare and handle ?)
yuga-na"ngala.m (yoke and plow)
asi-camma.m (sword and shield)
dhanu-kalaapa.m (bow and quiver)
hattha-(a)ssa-ratha-pattika.m (elephants, horses, chariots and infantry)
da.msa-makasa.m (gadflies and mosquitoes)
kuntha-kipillika.m (ants and (another kind of) ants)
kii.ta-siri.msapa.m (bugs and lizards)
ahi-nakula (the snake and the mongoose)
bi.laara-muusika.m (cat and mouse)
kaakoluuka.m (kaaka + uluuka.m) (crow and owl)
kusalaakusala.m (kusala + akusala.m) (good and evil)
siila-pa~n~naa.na.m (virtue and wisdom)
samatha-vipassana.m (tranquility and insight)
vijjaa-carana.m (knowledge and conduct)
saariputta-moggalaana.m (Saariputta and Moggalaana)
daasi-daasa.m (female and male slaves)
itthi-puma.m (woman and man)
patta-ciivara.m (bowl and robe)
tika-catukka.m (three and/or? four)
ve.na-rathakaara.m (bamboo workers and cartwrights, despised occupations)
saaku.nika-maagavika.m (fowlers and deerhunters)
diigha-majjhima (long and middle-lenthed)
Total number of dvandvas in sample: 29
Comprising two elements: 27
Comprising three elements: 1
Comprising four elements: 1
Final member longest: 21
First member longest: 0
All members equally long: 8
Of the 8 with members of equal length:
Have a member ending in i/u as first member: 5
Have a member ending in i/u as last member : 0
Consist only of -a stems: 3
Conclusions:
1) 'natural pair' neuter dvandvas always put the longest (by syllable count) member last.
2) If one member ends in i/u it always comes first in the sample, since these dvandvas probably have to be an -a stem neuter.
3) No cases where rule 2 has overriden rule 1 are in the sample. Hence it is likely that i/u endings can only occur where the i/u is either shortest or of equal length with the -a stem element.