  Dark matter halo clustering depends not only on halo mass, but also on other
properties such as concentration and shape. This phenomenon is known broadly as
assembly bias. We explore the dependence of assembly bias on halo definition,
parametrized by spherical overdensity parameter, $\Delta$. We summarize the
strength of concentration-, shape-, and spin-dependent halo clustering as a
function of halo mass and halo definition. Concentration-dependent clustering
depends strongly on mass at all $\Delta$. For conventional halo definitions
($\Delta \sim 200\mathrm{m}-600\mathrm{m}$), concentration-dependent clustering
at low mass is driven by a population of haloes that is altered through
interactions with neighbouring haloes. Concentration-dependent clustering can
be greatly reduced through a mass-dependent halo definition with $\Delta \sim
20\mathrm{m}-40\mathrm{m}$ for haloes with $M_{200\mathrm{m}} \lesssim
10^{12}\, h^{-1}\mathrm{M}_{\odot}$. Smaller $\Delta$ implies larger radii and
mitigates assembly bias at low mass by subsuming altered, so-called backsplash
haloes into now larger host haloes. At higher masses ($M_{200\mathrm{m}}
\gtrsim 10^{13}\, h^{-1}\mathrm{M}_{\odot}$) larger overdensities, $\Delta
\gtrsim 600\mathrm{m}$, are necessary. Shape- and spin-dependent clustering are
significant for all halo definitions that we explore and exhibit a relatively
weaker mass dependence. Generally, both the strength and the sense of assembly
bias depend on halo definition, varying significantly even among common
definitions. We identify no halo definition that mitigates all manifestations
of assembly bias. A halo definition that mitigates assembly bias based on one
halo property (e.g., concentration) must be mass dependent. The halo
definitions that best mitigate concentration-dependent halo clustering do not
coincide with the expected average splashback radii at fixed halo mass.
