  The Bochner-Riesz multipliers $ B_{\delta }$ on $ \mathbb R ^{n}$ are shown
to satisfy a range of sparse bounds, for all $0< \delta < \frac {n-1}2 $. The
range of sparse bounds increases to the optimal range, as $ \delta $ increases
to the critical value, $ \delta =\frac {n-1}2$, even assuming only partial
information on the Bochner-Riesz conjecture in dimensions $ n \geq 3$. In
dimension $n=2$, we prove a sharp range of sparse bounds. The method of proof
is based upon a `single scale' analysis, and yields the sharpest known weighted
estimates for the Bochner-Riesz multipliers in the category of Muckenhoupt
weights.
