We prove the conjectural endoscopic transfer of L-packets for the local
Langlands correspondence for pure inner forms of unramified p-adic groups and
depth-zero parameters established by DeBacker and Reeder. More precisely, we
show that under mild conditions on the residual characteristic, endoscopic
induction identifies an unstable character of such an L-packet with the stable
character of the corresponding endoscopic L-packet.