Since I asked for advice about shortening, and people were kind enough
to reply, it seems appropriate to follow up and tell what happened next.

Here is the recipe I used:

<quote>

Soft Sugar Cookies

1 c. shortening
1 c. sugar
2 eggs
2 tsp. vanilla
2 1/4 c. sifted flour
1/2 tsp. soda
1 tsp. salt

Drop by spoon onto greased baking sheet. Bake until lightly browned.
Cookies should be soft. Cool slightly, then remove from baking sheet.
Bake 8 to 10 minutes at 375 degrees.

<end quote>

With many thanks to the posters who guided me to less than lethal
"shortening," I ran out and got some "0-trans fat Crisco," and will try
some butter and other oils in the future.

At about 7 minutes in the oven, all the cookies merged. They made
little grooves where they met. When I removed them from the oven, I
used a pizza cutter on the grooves. I didn't see this coming, because
the dough was really pretty stiff.

The cookies are very delicate, about 3" square. (I was hoping for little
rounded lumps, maybe 2 inches in diameter.)

I used an aluminum baking sheet, which I spritzed with a no-stick oil.
I mean, the recipe said to do that. But, apparently, I greased the holy
hell out of it, because the cookies are still moist on the bottoms. The
sheet, however, is quite clean.

The upside is that cookies are really, really good.