  Take a graph $G$, an edge subset $\Sigma\subseteq E(G)$, and a set of
terminals $T\subseteq V(G)$ where $|T|$ is even. The triple $(G,\Sigma,T)$ is
called a signed graft. A $T$-join is odd if it contains an odd number of edges
from $\Sigma$. Let $\nu$ be the maximum number of edge-disjoint odd $T$-joins.
A signature is a set of the form $\Sigma\triangle \delta(U)$ where $U\subseteq
V(G)$ and $|U\cap T)$ is even. Let $\tau$ be the minimum cardinality a $T$-cut
or a signature can achieve. Then $\nu\leq \tau$ and we say that $(G,\Sigma,T)$
packs if equality holds here.
  We prove that $(G,\Sigma,T)$ packs if the signed graft is Eulerian and it
excludes two special non-packing minors. Our result confirms the Cycling
Conjecture for the class of clutters of odd $T$-joins with at most two
terminals. Corollaries of this result include, the characterizations of weakly
and evenly bipartite graphs, packing two-commodity paths, packing $T$-joins
with at most four terminals, and a new result on covering edges with cuts.
