Spin Doctors - Two Princes

Yes - it's two edits and a very slightly early fade.

I was on a promo-for-jukeboxes service at the time, so
I have the LP version on Spotlight On Hits Pop Vol.
10 and the Edit on Hot Hits Pop Vol. 19.
I'm confident that these are digital clones of the
version from the actual promo CD single. The samples
line up throughout, so if I align the edited portions
correctly, I get partial cancellation. The Edit is
also about 4 dB louder than the LP version, with a
different EQ, and seems to have a small amount of
compression/limiting/clipping.

Here are editing instructions to recreate the Edit,
using the LP version on Spotlight On Hits Pop Vol.
10 as the source:

Segment 1
Extends from 0:00.0 to 0:06.8 of both the LP version
and the Edit
Ends on a snare

Remove the 16 beats from 0:06.8 to 0:16.2 of the LP
version.

Segment 2
Begins on a snare
Extends from 0:16.2 to 1:55.9 of the LP version
Extends from 0:06.8 to 1:46.6 of the Edit
Ends before a downbeat, immediately after the last tom
tom hit in the drum fill

Remove the 56 beats from 1:55.9 to 2:28.3 of the LP
version.

Segment 3
Begins slightly before the downbeat that starts the
word "marry"
Extends from 2:28.3 to 4:12.2 of the LP version
(shortens LP version by about 6 seconds)
Extends from 1:46.6 to 3:30.5 of the Edit

Fade
Starts about 8 beats before LP version fade starts
Begins on a true downbeat
Extends from 3:56.1 to 4:12.2 of the LP version
Extends from 3:14.5 to 3:30.5 of the Edit

Your mixdown will run 3:30.5, with edits at 0:06.8 and
1:46.6.

Back when this was current in 1993, we played only the
LP version. I didn't even know there was an edited
version until about four years ago, when the following
actually took place live on the air on Crap From
The Past:

Some commercial radio friends of mine were in town for
a conference, so I brought them all on my show all
together. Four other commercial radio heavyweights
sitting in on Crap From The Past - quite a
treat for me! We played a game called "Hit The Post",
where I'd play the intro of some very well-known pop
songs, and they'd talk over the song intro (the
"ramp", in radio lingo) and stop their talking when
the song vocals start (the "post"). This was how
songs were introduced on top 40 radio up until about
ten years ago. (Listen to some old American Top
40 shows, and you'll hear Casey doing the same
thing, except that his vocals were pre-taped and laid
over the song after-the-fact.)

So my radio friends are having a blast with this.
We're taking turns talking up the ramps to songs we
know well, like "Walking On Sunshine", "Urgent", and
"Love In An Elevator". When it was my friend Brad's
turn, he picked "Two Princes". I played the Hot
Hits version, which was the Edit, not knowing
there even WAS an edit of "Two Princes". Brad was
expecting 19 seconds of intro to work with, and was
baffled and mortified when the vocals kicked in at 10
seconds! I was even more mortified for accidentally
springing the Edit version on him, and apologized
profusely for the next minute or two. I'm certain
that he can recall the whole incident just as vividly
as I can - we never forget the really public
mistakes...

Did the one-track promo with the LP version come out
first?

I never even knew there was an edit of the song. I grew
up with the full length version and also have multiple
copies of the 45 (I never even knew a promo 45 existed).