Customizing page-links?

I was hoping someone could help me devise a method to customize page-links beyond what appears to be possible extending wp_link_pages().

Currently, my posts display the page links as follows:

Pages: 1 | 2 | 3 | 4 | 5 |
(The default treatment as twentyten as my parent theme.)

I’d rather be able to customize each link to be a bit more descriptive, for example:

Pages: Lorem ispum | Second page | Dolor sit amet

This would allow for each link to describe the content of the “page” as opposed to just the number.

How would one extend wp_link_pages() to handle a custom link for each “page?” Is there an alternative method that would be better suited?

Many thanks….. Paul