Out of memory error at upload step of mailing

At the upload step of sending a mailing in CiviMail, an out of memory error occurs. Initially discussed in the forum at http://forum.civicrm.org/index.php/topic,285.0.html.

To create this on my server which has 90M memory available (CiviMail not availabe on the demo), I did the following:
1. Initialize my contact database with 950 contacts
2. Select send a new mailing
3. Add a name to the mailing (Step 1)
4. Add a small group of one individual as the recipient (Step 2)
5. Uploaded a text message (2k) and html message (7k), then click upload (Step 3)
Then either blank screen occurs, or a screen with error messages indicating out of memory failure at various lines of code (not necessary the same one each time).

This problem does not occur when the number of contacts was reduced to 900, or with either the HTML or the TXT message was uploaded (but not both).