I thought this was already handled in core Druapl pretty well(without CCK or another text field).
Are you trying to do something different?

When creating/editing a node, you can click "Split Summary at Cursor" to manually create a teaser break-point.
Then, after creating the manual break-point, there is another option to "Show summary in full view." If that is checked (defualt), the teaser is displayed at the beginning of the content when you view the full node. When this option is unchecked, the teaser is not shown when viewing the full node, thus becomming an "alternate teaser."
Is that what you want?

Also, are you using a wysiwyg? They can modify this behavior slightly.

Alternate teasers were brought into core with Drupal 6. With Drupal 5, you should check out Excerpt.module.

Ahhhhhh... ok, that explains it. I am using (experimenting with, really) D6.
Clint must be using D5.

Actually, that's a new feature of D6 that I wasn't familiar with and is exactly what I'm looking for. Looks like my wheel's already been invented.

Now I understand why I didn't notice this before. I'm using TinyMCE/WYSIWYG API and while I've enabled the teaser break button, I can't find anything about an option to install a "Show summary in full view" checkbox.

Looks like it's time to hit the eject button on tinyMCE and WYSIWYG API. It sounds like most people here are recommending FCKeditor with the FCKeditor module. Are there other WYSIWYG options that work with these new D6 features?

In Drupal 5.x I'd recommend using the Node Teaser module (http://drupal.org/project/nodeteaser). This is an alternative to Node Excerpt.

I am using FCKeditor and FCKeditor module.
Teaser functionality seems to work properly.