  We prove an achievability result for privacy amplification and decoupling in
terms of the sandwiched R\'enyi entropy of order $\alpha \in (1,2]$; this
extends previous results which worked for $\alpha=2$. The fact that this proof
works for $\alpha$ close to 1 means that we can bypass the smooth min-entropy
in the many applications where the bound comes from the fully quantum AEP or
entropy accumulation, and carry out the whole proof using the R\'enyi entropy,
thereby easily obtaining an error exponent for the final task. This effectively
replaces smoothing, which is a difficult high-dimensional optimization problem,
by an optimization problem over a single real parameter $\alpha$.
