  We analyze the conformal bootstrap constraints in theories with four
supercharges and a global $O(N) \times U(1)$ flavor symmetry in $3 \leq d \leq
4$ dimensions. In particular, we consider the 4-point function of
$O(N)$-fundamental chiral operators $Z_i$ that have no chiral primary in the
$O(N)$-singlet sector of their OPE. We find features in our numerical bounds
that nearly coincide with the theory of $N+1$ chiral super-fields with
superpotential $W = X \sum_{i=1}^N Z_i^2$, as well as general bounds on SCFTs
where $\sum_{i=1}^N Z_i^2$ vanishes in the chiral ring.
