Compression / Sustainer or Noise Reducer?

[nervousbreakdance]

Hi all,

I'm not really a bassist, but I have been playing bass for sometime with a band, and I use a pretty distinct effects set up: Danelectro 'Chilli Dog' Octave > Boss ODB Bass Overdrive > Electro Harmonix Big Muff > amp.

Anyone who has used a Big Muff, esp with bass, will know that despite sounding great, they can be really noisy. I has an idea about using a compressor or noise reducer at the start of the chain to give me a cleaner overall sound.

My question is, which should I be looking at? What will give the big muff a clearer signal?

Thanks in advance!