  Crossing symmetry (CS) is the main tool in the bootstrap program applied to
CFT models. This consists in an equality which imposes restrictions on the CFT
data of a model, i.e, the OPE coefficients and the conformal dimensions.
Reflection positivity (RP) has also played a role, since this condition lead to
the unitary bound and reality of the OPE coefficients. In this paper we show
that RP can still reveal more information, showing how RP itself can capture an
important part of the restrictions imposed by the full CS equality. In order to
do that, we use a connection used by us in a previous work between RP and
positive definiteness of a function of a single variable. This allows to write
constraints on the OPE coefficients in a concise way, encoding in the
conditions that certain functions of the crossratio will be positive defined
and in particular completely monotonic. We will consider how the bounding of
scalar conformal dimensions and OPE coefficients arise in this RP based
approach. We will illustrate the conceptual and practical value of this view
trough examples of general CFT models in $d$-dimensions.
