  Given a line bundle L on a smooth projective curve over the complex numbers,
we show that a general extension E of L by the trivial line bundle is very
stable: line bundles contained in E have degree much less than half the degree
of E. From this result we deduce new inequalities for the successive minima of
the euclidean lattice H^1(X,L^{-1}), where L is an hermitian line bundle on the
arithmetic surface X.
