The STrauss process is a point process with unnormalized density with respect to a Poisson point process, where each pair of points within a specified distance $r$ of each other contributes a factor $λ\in (0, 1)$ to the density. Basic Acceptance Rejection works spectacularly poorly for this problem, which is why several other perfect simulation methods have been developed. these methods, however, also work poorly for reasonably large values of $λ$. *Acceptance Rejection Stitching* is a new method that works much faster, allowing the simulation of point processes with values of $λ$ much larger than ever before.