I usually play 1.Nf3 f5 2.d3 Nc6 with the idea of 3.e4 e5 transposing to an innocuous variation of the Latvian gambit (1.e4 e5 2.Nf3 f5 3.d3?! Nc6).
I cannot find the Carlsen game in New In Chess at the moment but I am pretty sure that someone suggested 3.d3-d4!? in reply to 2...Nc6. Despite the loos of tempo, d4-d5 is a real threat. We don't want to play a Stonewall after 3...d5 so Black has to come up with something better.

As you might expect, I will not give up my pet defense very soon. After a short investigation:
1.Nf3 f5 2.d3 d6 3.e4 e5 4.Nc3
A) 4...Nf6 5.exf5
-5.d4 exd4 6.Nxd4 Nxe4 = according to Williams

5...Bxf5 6.d4 e4
-6...Nbd7 is equal (Williams) but what about 7.Bc4!? Maybe 7...Nb6 8.Bb3 e4 9.Nh4 Bg4.

7.Nh4
and according to Williams White is better; that is questionable after Bg4.

B) 4...Nc6 5.exf5
-5.Be2 Nf6 6.o-o Be7 7.Re1 o-o 8.Bf1 Appstrom-Biemann,1992, Qe8 9.d4 Nxe4 10.Bc4+ Kh8
11.dxe5 dxe5 12.Nxe4 fxe4 13.Rxe4 Bf5 with the initiative.

5...Bxf5 6.d4
-6.Be2 Be7 7.Be3 Nf6 8.o-o (8.a3 o-o 9.o-o d5) o-o 9.d4 a6 or Nxd4 =.

6...Nxd4 7.Nxd4 exd4 8.Qxd4 c6!
-8...Nf6 9.Bc4 is irritating, Carlsen-Dolmatov,2004.

9.Bf4
-As 9.Bc4 d5 is fine for Black and 9.Bd3 Bxd3 10.Qxd3 c6 transposes to Romanisjin-
Malanjuk, 1987, this is the only try.

9...Qf6
-9...Bxc2 10.Kd2 Bg6 (Bf5 seems even better) 11.Re1+ Kd7 12.g3 Seel-Horstmann,2003, Nf6
13.Bh3+ Kc7 looks like a good fight.

10.Qd2
Breutigam-Dirr,2004. Now 10...o-o-o is unclear.

C) Black should definitely not try 1.Nf3 f5 2.d3 Nf6? as 3.e4 is an improved version of the
Lisitsyn Gambit.
I also must admit that I do not like 1.Nf3 f5 2.d3 e6 3.e4 too much. So if Black wants to avoid
the Lisitsyn Gambit proper, 1...e6 might not be the right way.

[code]A) 4...Nf6 5.exf5 Bxf5 6.d4 Nbd7!? 
B) 3...Nf6 and 4...e6 and only after castling e6-e5.  MNb[/code]

What are the beginning moves in variation A)?  In the variation given by Losetowin Black has already played ...Nc6.

I'd assumed the second variation was bad for Black because of the continuation 1.Nf3 f5 2.d3 d6 3.e4 Nf6 4.exf5 Bxf5 5.d4 and Black can't get in ...e5 smoothly.  But I'd be willing to listen if anybody thinks Black is OK in that position.

I have a really hard time believing 2.d3 is a serious threat to 1...f5 versus 1.Nf3.  I'm sure the Philidor-Countergambit is unsound, but with an extra tempo it should be playable.  I have a feeling you might be right about 4...Nc6 being incorrect due to White being able to play d5 at some point with tempo.  I think possibly 4...Nf6 is better.  There is a NIC article on this that I don't have access to.  Can anyone tell us about alternatives to 4...Nc6 or improvements for Black in this line?