I want to be able to see the search query in the URL, and have a URL that I can always go back to if I restart my browser. I set the HTTP request method in settings to GET instead of POST since that shows the query, but it adds a bunch of extra paramters:
I just installed ClearURLs and it still has the tracking parameters, can I add parameters to the addon for it to remove?
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Agreed. Further, I doubt any of the OP’s examples are tracking. lui=english just means to have the page use english (not spanish, chinese, etc.), cat=web means not shopping, news or anything like that – just a web search, and while I;m not sure about device, I THINK that refers to whether the result should be formatted for phone, desktop, or such.