  Stressed nanomechanical resonators are known to have exceptionally high
quality factors ($Q$) due to the dilution of intrinsic dissipation by stress.
Typically, the amount of dissipation dilution and thus the resonator $Q$ is
limited by the high mode curvature region near the clamps. Here we study the
effect of clamp geometry on the $Q$ of nanobeams made of high-stress
$\mathrm{Si_3N_4}$. We find that tapering the beam near the clamp - and locally
increasing the stress - leads to increased $Q$ of MHz-frequency low order modes
due to enhanced dissipation dilution. Contrary to recent studies of
tethered-membrane resonators, we find that widening the clamps leads to
decreased $Q$ despite increased stress in the beam bulk. The tapered-clamping
approach has practical advantages compared to the recently developed
"soft-clamping" technique. Tapered-clamping enhances the $Q$ of the fundamental
mode and can be implemented without increasing the device size.
