By considering a class of diagrams which has been overlooked also in the mo
st recent literature on three-body forces, we extract a new contribution to
the three-nucleon interaction which specifically acts on the tripler odd s
tates of the two-nucleon subsystem. In the static approximation, this 3N-fo
rce contribution is fixed by the underlying 2N interaction, so in principle
there are no free parameters to adjust. The 2N amplitude however enters in
the 3NF diagram in a form which cannot be directly accessed or constrained
by NN phase-shift analysis. We conclude that this new 3N-force contributio
n provides a mechanism which implies that the presence of the third nucleon
modifies the p-wave (and possibly the f-wave) components of the 2N subsyst
em in the triplet-isotriplet channels.