  We exhibit some (compact and cusped) finite-volume hyperbolic four-manifolds
M with perfect circle-valued Morse functions, that is circle-valued Morse
functions $f\colon M \to S^1$ with only index 2 critical points. We construct
in particular one example where every generic circle-valued function is
homotopic to a perfect one.
  An immediate consequence is the existence of infinitely many finite-volume
(compact and cusped) hyperbolic 4-manifolds $M$ having a handle decomposition
with bounded numbers of 1- and 3-handles, so with bounded Betti numbers
$b_1(M)$, $b_3(M)$ and rank of $\pi_1(M)$.
