  We introduce the notion of confinement of decompositions for forms or vector
of forms. The confinement, when it holds, lowers the number of parameters that
one needs to consider, in order to find all the possible decompositions of a
given set of data. With the technique of confinement, we obtain here two
results. First, we give a new, shorter proof of a result by London
(\cite{London90}) that $3$ general plane cubics have $2$ simultaneous Waring
decompositions of rank $6$. Then we compute, with the software Bertini, that
$4$ general plane quartics have $18$ different decompositions of rank $10$ (a
result which was not known before).
