I'm going nuts here ...

... there's probably a simple answer but I can't see it.
I would like to have a different sidebar on every page. I have downloaded and installed the 'Page sidebars' plugin and it works fine on every page, except for the Home.
Either I get nothing. Or, if I add a text widget, that text appears, additionally, on every other page too.
I have tried changing the 'Front page displays' on the 'Reading' panel to 'Static Page', and chosen a page, but then I get that page twice - once as itself and once as Home.
How can I get a unique Home page that displays a unique sidebar? The only way I can see is to create a page with no title (so it doesn't show on the navigation bar), select it as the static front page and put it next to Home. But that doesn't seem very elegant.
Thanks