Hi Richard (again),
I tried again, with CCleaner. No luck.
BUT, I should explain a bit more.
The kind of browsing history I am trying to erase is what some people on this site call the 'breadcrumb history', which shows which websites you've visited, in the past.
If I type in the first few letters of a website I want to go to, the IE browser window also shows me all of the (other) websites that start with those letters etc., in a 'history' list. This is what I want to erase.
In other words, CCleaner etc. may erase (or hide) from the browser's history websites I've visited minutes, or hours ago. But as soon as I type into the browser any letters that begin the address of any website I've visited ... any time, the browsing history shows it.
Any ideas how I can erase this? I really appreciate your help.