  About twenty years ago Johnson and Zippin showed that every separable
L_1(mu)-predual was isometric to a quotient of C(Delta ), where Delta is the
Cantor set. In this note we will show that the natural analogue of the theorem
for l_1-preduals does not hold. We will show that there are many l_1-preduals
which are not isometric to a quotient of any C(K)-space with K a countable
compact metric space. We also prove some general results about the relationship
between l_1-preduals and quotients of C(K)-spaces with K a countable compact
metric space.
  The results in this paper were presented at the Workshop on Banach Space
Theory in Merida, Venezuela, January 1992.
