For systems that are neither fully integrable nor fully chaotic, bifurcatio
ns of periodic orbits give rise to semiclassically emergent singularities i
n the fluctuating part N-fl of the energy-level counting function. The bifu
rcations dominate the spectral moments
M-m((h) over bar)= [(N-fl)(2m)]
in the limit (h) over bar --> 0. We argue that M-m((h) over bar) similar to
const./(h) over bar(nu m), and calculate the twinkling exponents nu(m) as
the result of a competition between bifurcations with different codimension
s and repetition numbers.