We consider the problem of finding all the “embeddings” of a discrete series representation in the principal series in the case of a simple real Lie group G of real rank one. More precisely, we solve the problem when G is
Spin
(
2
n
,
1
)
,
SU
(
n
,
1
)
,
SP
(
n
,
1
)
or
F
4
(
n
⩾
2
)
\operatorname {Spin} (2n,\,1),{\text {SU}}(n,\,1),\,{\text {SP}}(n,\,1)\,{\text {or}}\,{F_4}\,(n\, \geqslant \,2)
. The problem is reduced to considering only discrete series representations with trivial infinitesimal character, by means of tensoring with finite dimensional representations. Various other techniques are employed.