Trying to create a disco ball using cycles

Hi guys!
I’m pretty new to Blender and I try to make a disco ball.
What I would like is that the ball “reflects” the lights on the wall (you know, those little spots of lights reflected by each square of a disco ball).
I’m using cycles and the material for the little mirror squares is
Glossy BSDF
Roughness 0

But :

  1. I got fireflies
  2. No lights are reflected onto the walls.

The spotlight I used is an object which emits white color (material->emission), stuck into a cylinder with an holdout material.

Does anyone knows how I could improve this ?
Thanks a lot !

Here’s the blend