Short-range correlated uniform noise in the dispersion coefficient, inheren
t in many types of optical fibers, broadens and eventually destroys all ini
tially ultra-short pulses. However, under the constraint that the integral
of the random component of the dispersion coefficient is set to zero (pinne
d), periodically or quasiperiodically along the fiber, the dynamics of the
pulse propagation changes dramatically. For the case that randomness is pre
sent in addition to constant positive dispersion, the pinning restriction s
ignificantly reduces average pulse broadening. If the randomness is present
in addition to piece-wise constant periodic dispersion with positive resid
ual value, the pinning may even provide probability distributions of pulse
parameters that are numerically indistinguishable from the statistically st
eady case. The pinning method can be used to both manufacture better fibers
and upgrade existing fiber links.