  We apply recently constructed functional bases to the numerical conformal
bootstrap for 1D CFTs. We argue and show that numerical results in this basis
converge much faster than the traditional derivative basis. In particular,
truncations of the crossing equation with even a handful of components can lead
to extremely accurate results, in opposition to hundreds of components in the
usual approach. We explain how this is a consequence of the functional basis
correctly capturing the asymptotics of bound-saturating extremal solutions to
crossing. We discuss how these methods can and should be implemented in higher
dimensional applications.
