  Let $G$ be an unweighted $n$-node undirected graph. A \emph{$\beta$-additive
spanner} of $G$ is a spanning subgraph $H$ of $G$ such that distances in $H$
are stretched at most by an additive term $\beta$ w.r.t. the corresponding
distances in $G$. A natural research goal related with spanners is that of
designing \emph{sparse} spanners with \emph{low} stretch.
  In this paper, we focus on \emph{fault-tolerant} additive spanners, namely
additive spanners which are able to preserve their additive stretch even when
one edge fails. We are able to improve all known such spanners, in terms of
either sparsity or stretch. In particular, we consider the sparsest known
spanners with stretch $6$, $28$, and $38$, and reduce the stretch to $4$, $10$,
and $14$, respectively (while keeping the same sparsity).
  Our results are based on two different constructions. On one hand, we show
how to augment (by adding a \emph{small} number of edges) a fault-tolerant
additive \emph{sourcewise spanner} (that approximately preserves distances only
from a given set of source nodes) into one such spanner that preserves all
pairwise distances. On the other hand, we show how to augment some known
fault-tolerant additive spanners, based on clustering techniques. This way we
decrease the additive stretch without any asymptotic increase in their size. We
also obtain improved fault-tolerant additive spanners for the case of one
vertex failure, and for the case of $f$ edge failures.
