Cannot edit PDF / unreadable characters in Adobe Illustrator

Hello forum members, hope someone can help me:

I have created PDF files with the latest version of PDFCreator, using both standard settings and changing Adobe compatibility versions (5.0, 6.0).

The PDF files display and print fine. However: When I try to edit them with Adobe Illustrator, all text is converted into non-readable characters (mostly question marks and boxes and the like). Illustrator complains about fonts that needed to be converted. Obviously, the conversion fails.

What settings need to be used to enable editing of PDF files with Illustrator? Or what else might be the reason for this behaviour?

Any help would be appreciated.

Thanks. Karl.