  We reformulate the heptagon cluster bootstrap to take advantage of the
Steinmann relations, which require certain double discontinuities of any
amplitude to vanish. These constraints vastly reduce the number of functions
needed to bootstrap seven-point amplitudes in planar $\mathcal{N} = 4$
supersymmetric Yang-Mills theory, making higher-loop contributions to these
amplitudes more computationally accessible. In particular, dual superconformal
symmetry and well-defined collinear limits suffice to determine uniquely the
symbols of the three-loop NMHV and four-loop MHV seven-point amplitudes. We
also show that at three loops, relaxing the dual superconformal ($\bar{Q}$)
relations and imposing dihedral symmetry (and for NMHV the absence of spurious
poles) leaves only a single ambiguity in the heptagon amplitudes. These results
point to a strong tension between the collinear properties of the amplitudes
and the Steinmann relations.
