Jonathan,
Thought you would like this given our experiments with turning speech into sinusoids and back again:
http://www.mrc-cbu.cam.ac.uk/people/matt.davis/sine-wave-speech/
I recall you saying you were able to recognise speech with only 3 sinusoids and I had a similar result. This study says that's probably not a very generalisable result.
Cheers,
Chris.