Extreme Lag With Minecraft?

I have been having a lot of lag with Minecraft even though my computer has great specs. Here are the specs.

6GB DDR3 Ram
2.9 Dual Core Hyper Threaded Intel I3 530 Processor
Intel I3 Graphics.
Windows 7 Home Premium

My computer plays other games perfectly, and doesn't lag with them, it is only Minecraft. Optifine does help a bit, but I want to use a mod, and it will not work with Optfine installed. Can anyone give me any suggestions on how I can fix it? I know it is not the computer.

Minecraft is a really unstable game just try turning down some settings, defrag your harddrive and reinstall minecraft (delete.minecraft folder)

If you have 64x java and minecraft is using it then its your computer. That computer isn't great, it has integrated graphics, there's no such thing as "Intel i3 graphics" there's only Intel HD graphics, which are bad for any game. The fact that you can play heavier games is a mystery, or at least with a good FPS.

What's your graphics card?

I have a Toshiba laptop with an i3 GPU and I will tell you it is the worst thing in the world. It would be nice to know the GHz on your processor. Anything less than a 2.4 sucks for Minecraft. Also, just turn down some of the Video Settings on Minecraft, meaning make them fast, not fancy. Make your Max Framerate to Unlimited. Don't make your Render Distance any higher than 8. Hope this helps.

Graphics card?