  We provide a uniform construction of $L^2$-models for all small unitary
representations in degenerate principal series of semisimple Lie groups which
are induced from maximal parabolic subgroups with abelian nilradical. This
generalizes previous constructions to the case of a maximal parabolic subgroup
which is not necessarily conjugate to its opposite, and hence the previously
used Jordan algebra methods have to be generalized to Jordan pairs.
  The crucial ingredients for the construction of the $L^2$-models are the Lie
algebra action and the spherical vector. Working in the so-called Fourier
transformed picture of the degenerate principal series, the Lie algebra action
is given in terms of Bessel operators on Jordan pairs. We prove that precisely
for those parameters of the principal series where small quotients occur, the
Bessel operators are tangential to certain submanifolds. Further, we show that
the small quotients are unitarizable if and only if these submanifolds carry
equivariant measures. In this case we can express the spherical vectors in
terms of multivariable K-Bessel functions, and some delicate estimates for
these Bessel functions imply the existence of the $L^2$-models.
