  We present a new and compelling approach to the efficient solution of
important computational problems that arise in the context of abstract
argumentation. Our approach makes known algorithms defined for restricted
fragments generally applicable, at a computational cost that scales with the
distance from the fragment. Thus, in a certain sense, we gradually augment
tractable fragments. Surprisingly, it turns out that some tractable fragments
admit such an augmentation and that others do not.
  More specifically, we show that the problems of credulous and skeptical
acceptance are fixed-parameter tractable when parameterized by the distance
from the fragment of acyclic argumentation frameworks. Other tractable
fragments such as the fragments of symmetrical and bipartite frameworks seem to
prohibit an augmentation: the acceptance problems are already intractable for
frameworks at distance 1 from the fragments.
  For our study we use a broad setting and consider several different
semantics. For the algorithmic results we utilize recent advances in
fixed-parameter tractability.
