[Dixielandjazz] when lyrics don't rhymez

[Bill Haesler]

eupher dude wrote (in part]:
 >I have in mind one particular recording of "Stepping Out", performer  
shall remain nameless from me at least, where the lyric is "Stepping  
out, taking air/ stepping out, on a tear".  The singer pronounces  
"tear" as used in crying, not (as I would assume would be best) as a  
rip.<

Dear Steve,
Which "Stepping/Steppin' Out" song are you referring to?
There appears to be several with this title, none of which (that I can  
find) use the line you quote.
There is a 1923 (John S Howard, lyrics - Con Conrad, music)  
composition recorded (minus lyrics) by Fletcher Henderson, Ted Lewis,  
Original Memphis 5 and others at that time.
So far as the Irving Berlin composition 1911/12 "At The Devil's Ball"  
the line you quote is wot he wrote.
Sorry about that.  8>)
1st chorus:
At the Devil's Ball
At the Devil's Ball
I saw the cute Missus Devil, so pretty and fat
Dress'd in a beautiful fireman's hat
Ephraham, the Leader man, who led the band last fall
He play'd the music at the Devil's Ball
In the Devil's hall
I saw the funniest devil that I ever saw
Taking the tickets from folks at the door
I caught a glimpse of my mother-in-law
Dancing with the Devil
Oh! the little Devil
Dancing at the Devil's Ball

In the context of Tin Pan Alley rhyming, it fits. Well, for me anyway.
For anyone interested in this subject (and especially for new young  
singers) I always recommend a 1990 book 'The Poets Of Tin Pan Alley'  
by Phillip Furia (Oxford University Press).
A great read, and a wonderful eye-opening insight into what it was all  
about in 'the old daze'.
Unfortunately, your two nominated songs aren't included.
Very kind regards,
Bill.