  We construct taut foliations in every closed 3-manifold obtained by
$r$-framed Dehn surgery along a positive 3-braid knot $K$ in $S^3$, where $r <
2g(K)-1$ and $g(K)$ denotes the Seifert genus of $K$. This confirms a
prediction of the L-space Conjecture. For instance, we produce taut foliations
in every non-L-space obtained by surgery along the pretzel knot $P(-2,3,7)$,
and indeed along every pretzel knot $P(-2,3,q)$, for $q$ a positive odd
integer. This is the first construction of taut foliations for every
non-L-space obtained by surgery along an infinite family of hyperbolic L-space
knots. Additionally, we construct taut foliations in every closed 3-manifold
obtained by $r$-framed Dehn surgery along a positive 1-bridge braid in $S^3$,
where $r <g(K)$.
