iTunes Sync Problem

Every time I try to sync my iPhone with iTunes, there are always a bunch of MP3 songs (about 35 of them) that won't sync, giving me the following error message:

[Song name] was not copied because the audio format is not supported by the iPhone [my iphone].

These songs have a high bit rate (e.g. 256 kbps) so I thought maybe iPhone doesn't support that. But when I checked the iPhone technical page I do see that it supports 256 kbps MP3 songs even with VBR. What's more, two songs from the same album do sync with no problem. That led me wonder what was wrong with the rest of the songs.

So I took my wife's iPhone and tried the same thing, the same problem happened. I tried my 2nd Generation iPod Nano, exactly the same problem. Here are the technical details of one of the songs that won't sync:

Kind: MPEG Audio File
Format: MPEG-1, Layer 2
Size: 9 MB
Channel: Stereo
Bit Rate: 256 kbps
ID3 Tag: v2.2
Sample Rate: 44.100 kHz
Encoded with: Unknown.

Here is the information for another song from the same album that strangely, sync with no problem:

Kind: MPEG Audio File
Format: MPEG-1, Layer 3
Size: 7.7 MB
Channel: Stereo
Bit Rate: 256 kbps
ID3 Tag: v2.2
Sample Rate: 44.100 kHz
Encoded with: Unknown.

The only difference I can see is Layer 2 vs. Layer 3 and I wonder if that could be the problem. If it is then what's the solution?

I am using iTunes 9.0.0.70 on Windows 7 with iPhone 3GS. Thanks in advance for ideas and help!