Timothy Taylor  in his book "Budapest Gambit" recommended:

1.d4 Nf6 2.c4 e5 3.e3!? (rehused gambit) Cc6! Transposition Tango (The white 3.e3 move becomes a waste of time and also encloses the QB).

Michael Ayton wrote on 11/06/12 at 12:34:11:

 
A fourth line, 9 ... a5, might be worth a shot.  After 10 Bd3, Black redeploys the knight to  c5, e.g., 10 ... Nf8, 11 0-0 N8d7, 12 b3 Nc5, 13 Be2 g6! (encouraging White to clog e4) 14 e4 Bg4 tending toward equality

Some variations of mine and two games I have found: 

3 ...e6!? -- fantastic! I never knew this opening existed! Who has pioneered it, and is there any theory? (I can see there are loads of transpositional possibilities ...) When I get time I might open a thread on it!

As regards the Tango, after 7 Qc2 d6!? 8 Bg5 Be7 9 e3, we now have three variations! Here are my thoughts so far:

I  9 ...Ng4!?. I am not sure I trust this, because of the line Vass gives above with 12 0-0! Nd7 13 b4 a5 14 a3 0-0 15 Ng5 Nb6. Here it seems 16 c5! leads to White pressure.

II  9 ...Nh7!?. In Raja-Arnaudov Black seemed OK after 10 Bd3 Ngf8 11 Be7 Qe7 12 c5!? dc 13 Nb5 Nf6 14 Qa4 Bd7 15 Bc4 Bb5 16 Qb5 N8d7 17 Qb7 0-0. But maybe White should try 12 Nb5 immediately? I haven't looked at this much -- it just looks a bit tedious, esp. for Black!

III  9 ...Nf8!?. The choice of Houdini, which gives the wonderful line 10 a3 N8h7 11 Bd3 g6 12 Bh6!? Ng4 13 Bg6 N7f6 14 Bg7 Rg8 15 Bf6 Nf6 16 Be4 Ne4 17 Qe4 f5 and Black is OK? Alternatively 10 Bd3 Nh7 here transposes to II, but blow me down, Houdini plays instead 10 ...N8d7. This seems to make no sense -- Black has lost four moves with his Queen's Knight! But then, can White claim any more than a slight edge? -- is it clear that the White c5 lever is going to be any more possible/dangerous than a Black ...f5?

I haven't looked at 8 ...Ne7 yet. I imagine White gets an advantage but you never know ...

Thank you very much, Vass -- about time I got acquainted with this simple technology!

I’m starting this thread in the hopes there might be others like me who are interested in exploring any newer developments in -- and White’s most dangerous lines against -- the Black Knights’ Tango. Thinking about why I often fail to look systematically at the recent games, I reckon this might be out of a feeling that White’s strongest tries involve not allowing a Tango at all, but heading for (e.g.) a Zurich Nimzo (the subject of another current thread). But the lines with an early h2-h4 (Chapter 2, pp. 42-54 of Richard Palliser's excellent 2005 book) strike me as no less dangerous than Tango-avoidance, and yet there are not many GM/IM games to look at.

The last development here I know about is the scare that arose in 2008 when linksspringer discovered that the line 1 d4 Nf6 2 c4 Nc6 3 Nc3 e5 4 d5 Ne7 5 Nf3 Ng6 6 h4 h5 7 e3 Bb4 8 Bd2 0-0 9 Bd3 Bc3? (Tango!, p. 47) 10 Bc3 e4 10 Bf6 Qf6 12 Be4 Qb2 is refuted by the simple 13 0-0!. Fortunately there was a rescue: 9 …d6!, after which 10 Ng5 (or 10 Qc2 Ne7) c6 11 Qc2 Ne7 should transpose to the line 9 Qc2 d6 10 Bd3 Ne7. 

Palliser implies 7 Qc2 here is a weaker choice for White, but I’m worried about the lines he gives: 7 …Ng4 8 Bg5 Be7 9 e3 d6 10 Bd3 Nf8 11 Be7 Qe7 12 0-0 [12 c5!?, 12 Nb5!?] is surely better for White even without the surely optimistic continuation 12 …g6?! 13 b4 f5? (14 e4!), and there’s also 9 d6!?, when 9 …cd 10 Nd5 Bg5 11 Ng5 Ne7 (p. 46) is fine for Black, but surely just 10 e3! (10 …0-0 11 Bd3; 10 …d5 11 cd) is stronger. (Houdini concocts a subtle defence beginning with 10 …b6!?, but it looks a bit thankless.) I therefore began to think just 7 …d6 might be best, meeting 8 Bg5 with 8 …Be7 9 e3 Nh7 (maybe 9 …Nf8 is possible too, e.g. 10 Bd3 N8d7 or 10 a3 N8h7), thus transposing into the line 7 Bg5 Be7 8 e3 d6 9 Qc2 (the book gives only 9 Bd3, which is also tricky though Black can avoid it with 7 ...d6 8 e3 [not forced!] Bf5) Nh7 (which got rather exciting in Raja-Arnaudov, Zagreb 2012). I also wondered about 7 Qc2 d6 8 Bg5 Ne7!?, while 7 ...Be7 is an alternative possibility, of course. 

White can also try (7 Qc2 d6) 8 Ng5!? here. I’m not sure how dangerous 8 …Be7 9 Ne6!? is, but maybe 8 …Ne7 is an idea here too? In many of these lines, though, the boundary between ‘solid’ and ‘nagging inferiority’ looks a hard one to see clearly, and I think Black has always to take care not to end up in a merely passive position. In short, 7 Qc2 looks to me a serious try, and I'm not at all sure what the best answer is.

This at any rate is my attempt to start the ball rolling on the more dangerous Tango lines. Any thoughts?