I will describe two recent results:
1. If the top-yukawa coupling is larger than (some geometric average of) the gauge couplings then the vacuum of the littlest higgs model does NOT contain an unbroken electroweak gauge group; and
2. The collective symmetry in the top-quark yukawa coupling is imposed "by hand," the model is fine tuned. There is no simple way to fix this (a precise statement will be given)