You don't need a Strict DOCTYPE for fixed support. You only need a DOCTYPE that triggers Standards Mode (or ‘almost standards’). That can be a transitional doctype such as:
<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN" "http://www.w3.org/TR/html4/loose.dtd">
or XHTML:
<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd">
as long as the system ID (the URI at the end) is included.
If your pages really are relying on Quirks Mode (ugh!), I'm sorry but you cannot use fixed and will have to resort to JavaScript hacks (but then you might need those for IE6 anyway).
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