  1) We give a 3-dimensional analogue of M. Noether's inequality for
canonically polarized threefolds: $K^3\ge 2(2p_g-5)/3$. This inequality is
sharp by known examples of M. Kobayashi.
  2) Given a minimal 3-fold $X$ of general type with canonical singularities,
if $K^3< (3p_g-5)/2$, we show that $X$ must be birationally fibred by curves of
genus 2.
