  Let p be a prime and suppose that K/F is a cyclic extension of degree p^n
with group G. Let J be the F_pG-module K^*/K^{*p} of pth-power classes. In our
previous paper we established precise conditions for J to contain an
indecomposable direct summand of dimension not a power of p. At most one such
summand exists, and its dimension must be p^i+1 for some 0<=i<n. We show that
for all primes p and all 0<=i<n, there exists a field extension K/F with a
summand of dimension p^i+1.
