  We show that smooth numbers are equidistributed in arithmetic progressions to
moduli of size $x^{66/107-o(1)}$. This overcomes a longstanding barrier of
$x^{3/5-o(1)}$ present in previous works of Bombieri-Friedlander-Iwaniec,
Fouvry-Tenenbaum, Drappeau, and Maynard. We build on Drappeau's variation of
the dispersion method and on exponential sum manipulations of Maynard,
ultimately relying on optimized Deshouillers-Iwaniec type estimates for sums of
Kloosterman sums.
