  Thin Lie algebras are Lie algebras L, graded over the positive integers, with
all homogeneous components of dimension at most two, and satisfying a more
stringent but natural narrowness condition modeled on an analogous one for
pro-p groups. The two-dimensional homogeneous components of L, which include
that of degree one, are named diamonds. Infinite-dimensional thin Lie algebras
with various diamond patterns have been produced, over fields of positive
characteristic, as loop algebras of suitable finite-dimensional simple Lie
algebras, of classical or of Cartan type depending on the location of the
second diamond. The goal of this paper is a description of the initial
structure of a thin Lie algebra, up to the second diamond.
  Specifically, if L_k is the second diamond of L, then the quotient L/L^k is a
graded Lie algebras of maximal class. In characteristic not two, L/L^k is known
to be metabelian, and hence uniquely determined up to isomorphism by its
dimension k, which ranges in an explicitly known set of possible values. The
quotient L/L^k need not be metabelian in characteristic two. We describe here
all the possibilities for L/L^k up to isomorphism. In particular, we prove that
k+1 equals a power of two.
