Is complexity an argument against design?

Interesting example Alasdair. Personally I am confused as to why complexity or simplicity should signify anything in terms of design or evolution. I also get lost as to what can be considered complex and what can be considered simple. Is the argument of ID supporters that if the world was "simple" in construction, whatever that word "simple" means, then there would be no ' designer' . Perhap if those of us who don't accept ID could somehow argue that the universe is "simple" then a cornerstone of ID would be lost. Could an ID proponent explain what is meant by "simple" and "complex" in terms of the ID debate, and also how "complexity" supports the presence of a designer, but the existence of "simplicity" does not.