  Verification of properties expressed as $\omega$-regular languages such as
LTL can benefit hugely from stutter insensitivity, using a diverse set of
reduction strategies. However properties that are not stutter invariant, for
instance due to the use of the neXt operator of LTL or to some form of counting
in the logic, are not covered by these techniques in general. We propose in
this paper to study a weaker property than stutter insensitivity. In a stutter
insensitive language both adding and removing stutter to a word does not change
its acceptance, any stuttering can be abstracted away; by decomposing this
equivalence relation into two implications we obtain weaker conditions. We
define a shortening insensitive language where any word that stutters less than
a word in the language must also belong to the language. A lengthening
insensitive language has the dual property. A semi-decision procedure is then
introduced to reliably prove shortening insensitive properties or deny
lengthening insensitive properties while working with a \emph{reduction} of a
system. A reduction has the property that it can only shorten runs. Lipton's
transaction reductions or Petri net agglomerations are examples of eligible
structural reduction strategies. We also present an approach that can reason
using a partition of a property language into its stutter insensitive,
shortening insensitive, lengthening insensitive and length sensitive parts to
still use structural reductions even when working with arbitrary properties. An
implementation and experimental evidence is provided showing most non-random
properties sensitive to stutter are actually shortening or lengthening
insensitive.
