How can I convert 60FPS videos to work on an iPhone 4? I have some 60 FPS videos ranging from 640x480 to 1280x720.  I was able to convert a few using H.264 Baseline @ L3.0 and sync them to Photo Albums on the iPhone and they clearly are playing back at 60 FPS.  The smoothness is incredible.  

Apple's tech specifications claim the iPhone can playback up to 30 FPS, but evidently this is not a true limitation.

My problem is most 60 FPS videos I have, fail to sync in iTunes and I get a message saying this video is not playable on the iPhone.  

What do I need to do differently to make 60 FPS videos reliably convert to iPhone 4 compatible H.264?  

Tools like MediaCoder iPod Edition and Any Video Converter tend to either force 30 FPS (A.V.C.) or crash outright when handling 60 FPS videos (MediaCoder which uses the x264 project to do the converting).
I use Handbrake to encode my files to iPhone and iPad specs.  Handbrake has presets for all the major Apple devices, so you don't even need to know the specifications for each device.  It even differentieates between an iPhone before the iPhone 4 and an iPhone 4.  Works every time for me.