  Available energy (\AE{}), which quantifies the maximum amount of thermal
energy that may be liberated and converted into instabilities and turbulence,
has shown to be a useful metric for predicting saturated energy fluxes in
trapped-electron-mode-driven turbulence. Here, we calculate and investigate the
\AE{} in the analytical tokamak equilibria introduced by
\citet{Miller1998NoncircularModel}. The \AE{} of trapped electrons reproduces
various trends also observed in experiments; negative shear, increasing
Shafranov shift, vertical elongation, and negative triangularity can all be
stabilising, as indicated by a reduction in \AE{}, although it is strongly
dependent on the chosen equilibrium. Comparing \AE{} with saturated energy flux
estimates from the \textsc{tglf} model, we find fairly good correspondence,
showcasing that \AE{} can be useful to predict trends. We go on to investigate
\AE{} and find that negative triangularity is especially beneficial in
vertically elongated configurations with positive shear or low gradients. We
furthermore extract a gradient threshold-like quantity from \AE{} and find that
it behaves similarly to gyrokinetic gradient thresholds: it tends to increase
linearly with magnetic shear, and negative triangularity leads to an especially
high threshold. We next optimise the device geometry for minimal \AE{} and find
that the optimum is strongly dependent on equilibrium parameters, e.g. magnetic
shear or pressure gradient. Investigating the competing effects of increasing
the density gradient, the pressure gradient, and decreasing the shear, we find
regimes that have steep gradients yet low \AE{}, and that such a regime is
inaccessible in negative-triangularity tokamaks.
