Particles are clumping on each frame I have tried using the Subframes option. It hasn't done a thing.

So I have an object which gives off 3 particles into the air.  I have an Icosphere object on a different layer with a particle instance modifier on it.  That allows me to add a particle system to the Icosphere to create some awesome particle trails



But the particle system that is attached to the Icosphere creates clumps of particles on each frame.  I am wanting a nice, smooth stream of particles being emitted from the main particles.

Is there a way to fix this, or does the Subframes option not work with the Particle Instance modifier.

Here is my .blend file: https://db.tt/DhdNlo3h
I am using Blender 2.72
To increase the accuracy and smoothness of simulations it can sometimes be helpful to scale the time up. 

Here a simple way of approximately stretching the time by 10. For every Particlesystem (3 in your example) multiply the End and the Lifetime of the emission by 10.



and divide the Timestep of the physics by 10.



In render settings multiply the End Frame and Frame Step by the same amount (10).



And render the frames as images. For videos you can reimport the frames in the VSE as image strip and render with the desired fps.