Render problem with custom particles and shadows

Hey everyone!
Dont know if this is “basic” but since this is my 3 week with blender it should be.
Anyway I am working on a short animaiton with a rocket that lifts of and blows up.
Everything is done and rendered exept for some timing.

I have a sligt problem with my particles.
When I turned on shadows for my lights it works fine for the solid objects but the custom particles that create my smoke and fire doesnt render correct shadows.

I have linked a picture where you can see what is happening.
There are three lights with shadows turned on in the scene.
As you can see the rocket makes asmooth and light shadow of to the right.
Just like I want it but the smoke looks awfull with shadows turned on.

Here is also a link to my blender file. Please help me. I am sort of in a hurry.
Anyone know just anything about what the problem might be then please tell me.

Blender file: