The BDG-style responses may be controversial but they are, indeed, a possibility.
1.e4 c6 2.d4 d5 3.Nc3 dxe4
4.Bc4 Nf6 5.f3 was met by 5...b5!? by Bareev against Short some years ago. 6.Bb3 a6 7.fxe4 b4 8.Na4 (8.Nce2, as played by Short, 8...Nxe4 9.Nf3 Be6 10.0-0 Bd6, =+) 8...Nxe4 9.Qf3 Nf6 (9...Qxd4 10.Ne2 Be5 11.Bf4 is probably a pawn too far) 10.Ne2 Ba6 11.Bg5 (or 11.c4 bxc3 12.Naxc3) with decent compensation. Alternatively Eric Schiller's preference 5...Qa5 allows White good compensation after 6.Bd2!.
Instead Stefan Bucker covered 5...exf3 6.Nxf3 Bf5 in a recent online article, 7.Bg5 e6 (else 8.Qe2 and 9.0-0-0, with sufficient compensation) 8.Nh4 leading to a dynamically equal position.
The other alternative is
4.f3, which I have used in quite a few games, most opponents take the f-pawn, when after 4...exf3 5.Nxf3 Nf6, White can choose between 6.Bd3 and 6.Bc4 transposing to 4.Bc4 Nf6 5.f3 exf3 6.Nxf3. The problem with 4.f3 is traditionally 4...e5, but Tim McGrew made quite a strong case for 5.Be3
http://www.chesscafe.com/text/mcgrew02.pdf (unlike in the Lemberger, Black cannot use the c6-square for the knight, so 5...exd4 6.Bxd4 doesn't quite work for Black). 5...Bb4 6.Bc4 Bxc3+ 7.bxc3 Qa5 (a possible improvement on McGrew's 7...exd4) 8.Ne2 exf3 9.0-0 with sharp and unclear play.
Alternatively 4.f3 Nf6 transposes to O'Kelly's defence to the BDG when White should transpose with 5.Bc4 as there are quite a few lines that defuse 5.Nxe4 (McGrew's analysis goes 5...Nxe4 6.fxe4 e5 7.Nf3 exd4?!- instead 7...Be6!, or 5...e5, which I discovered independently, or 5...Nbd7, proposed by someone else on this forum).