If
p
p
is an odd prime that does not divide the class number of the imaginary quadratic field
k
k
, and the cyclotomic
Z
p
{\mathbb {Z}_p}
-extension of
k
k
has
λ
\lambda
-invariant less than or equal to two, we prove that every totally ramified
Z
p
{\mathbb {Z}_p}
-extension of
k
k
has
μ
\mu
-invariant equal to zero and
λ
\lambda
-invariant less than or equal to two. Combined with a result of Bloom and Gerth, this has the consequence that
μ
=
0
\mu = 0
for every
Z
p
{\mathbb {Z}_p}
-extension of
k
k
, under the same assumptions. In the principal case under consideration, Iwasawa’s formula for the power of
p
p
in the class number of the
n
n
th layer of a
Z
p
{\mathbb {Z}_p}
-extension becomes valid for all
n
n
, and is completely explicit.