  Klopsch and the author have constructed a finitely generated pro-p group G,
for p an odd prime, with infinite normal Hausdorff spectrum with respect to the
p-power series. They show that the normal Hausdorff spectrum of G contains an
infinite interval, which answers a question of Shalev.
  They indicate in their paper how their results extend to the case p=2. In
this note, we provide all the details for the even case.
