A hybrid of Fake Nationality and Not Even Bothering With The Accent in which actors whose first language is something other than English are cast as characters whose first language is something else other than English. They speak English with an accent, but not the accent that would actually be logical for the character. (Note that at the moment I'm only looking at this from an (American) English-speaking perspective. Any information on whether/how this occurs in other languages would be appreciated.)

Probably occurs for two reasons. First (an assumption on my part; can anyone confirm?) is that someone who cannot speak a language unaccented would probably have difficulty speaking it with a different "foreign" accent. Second is that viewers presumably can't tell the difference anyway, so why let an accent stand in the way of casting the best actor on hand?

Seems most common in old Hollywood films, although I'm sure more recent examples will come to light.

Examples:

• Peter Lorre (Austrian accent) as a variety of non-German-speaking nationalities: Greek in The Maltese Falcon, Italian in Casablanca, Dutch in The Mask of Dimitrios, Japanese in the Mr. Moto films, and probably others.
• Bela Lugosi (Hungarian accent) as Dracula (Romanian).
• Possible subversion: In Twins Arnold Schwarzenegger used a "high German" accent instead of his usual Austrian accent to suggest a highly educated personality.
• Mira Furlan (Croatian accent) as a Frenchwoman on Lost.

Related (though perhaps not strictly within the confines of this trope) are the ideas that RP can substitute for any British accent, and that a British accent can substitute for the accents of characters whose first language is not English.

Rolling Updates.

Edit: Changed title from "As Long As It's A Foreign Accent" to "Interchangeable Accents," which may or may not be an improvement.

Edited to bump, November 4th.