I've always called this version of the dance Jefferson & Liberty. Now, looking on line, it looks like Jefferson & Liberty goes:
A1 Circle left, right
A2 Star right, left
B1 Ones down center, turn alone, return, cast around twos
B2 Four (slow) changes of Rights & Lefts

(In ECD terms, four changes of a circular hey with hands)

There's another variant of Jefferson and Liberty by Carlotta Wellington. It works well as a beginning dance for people who want to include a swing:

Taking Liberties with Jefferson
    Carlotta Wellington
A1 Circle left, right
A2 Star right, left
B1 Down Hall 4 in line--ones in center
      Ones, twos duck under
      Return in twos, Twos in front, Ones behind
B2 All balance & swing, end facing the next couple

erik hoffman
    oakland, ca


On 3/5/2016 10:54 AM, Jonathan Sivier jsivier@illinois.edu [trad-dance-callers] wrote:
 

On 3/5/2016 12:44 PM, Rich Sbardella richsbardella@gmail.com
[trad-dance-callers] wrote:
>
>
> I rarely call a contra at a One Night Party Dance, but occasionally I am
> asked to. I have a few in my cards, but can anyone make some sure fire
> recommendations.
>
> Assume 95%-100% non dancers.
>

I like to use Jefferson's Reel. There is usually an "ah ha" moment
when the 2's duck through the arches and meet their new neighbors and
everyone suddenly realizes how progression is supposed to work. I've
even done this with a rolling start with non-dancers with a lot of
success. Do it as a proper dance to avoid any need to deal with
crossing over at the ends or even worrying about who is dancing the
gent's or lady's part.

Jefferson's Reel
Dudley Briggs; adapted from Jefferson and Liberty
duple proper or improper; beginner

1 - Circle left
2 - Circle right
3 - Star right
4 - Star left
5 - 1's down the outside
6 - Return to place
7 - Down the hall 4 in line, 1's in the center
8 - All back up, 1's arch joined hands,
2's duck through the arch to meet new neighbors

Jonathan
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Jonathan Sivier
Caller of Contra, Square, English and Early American Dances
jsivier AT illinois DOT edu
Dance Page: http://www.sivier.me/dance_leader.html
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Q: How many angels can dance on the head of a pin?
A: It depends on what dance you call!