0: Match anywhere (e.g., middle of words)
1: Match on word boundaries, then match anywhere (default)
2: Match only on word boundaries (e.g., after / or .)
3: Match at the beginning of the url or title

Not exactly. There is a hidden preference for how to match domains and page titles in the autocomplete drop-down (you can modify this in the about:config preferences editor): browser.urlbar.matchBehavior 0: Match anywhere (e.g., middle of words) 1: Match on word boundaries, then match anywhere (<u>default</u>) 2: Match only on word boundaries (e.g., after / or .) 3: Match at the beginning of the url or title Since the dot in google''.''se is a word boundary, only 3 is likely to help in this case. I didn't notice any change when choosing 3, but maybe I needed to restart Firefox after modifying it? The ''sequence of results'' in the autocomplete drop-down, which might also affect the in-URLbar-autofill feature, is based largely on something called frecency (frequency + recency). It's possible to adjust the way Firefox computes frecency by giving more or less weight to sites based on how you visit them: by link, by typing, etc. https://developer.mozilla.org/en-US/docs/The_Places_frecency_algorithm If you visit Google a lot, this might not make enough difference to change what you're getting. Finally, if you want to erase Firefox's history just for google.se, that is possible using the "Forget about this site" feature. Note that this also will remove site-specific permissions and bookmarks. If that's of interest, I can explain it in more detail.

You can also consider to use a keyword in combination of a bookmark See also: *http://kb.mozillazine.org/Location_Bar_search *http://kb.mozillazine.org/browser.urlbar.matchBehavior