  Superconducting quantum technologies require qubit systems whose properties
meet several often conflicting requirements, such as long coherence times and
high anharmonicity. Here, we provide an engineering framework based on a
generalized superconducting qubit model in the flux regime, which abstracts
multiple circuit design parameters and thereby supports design optimization
across multiple qubit properties. We experimentally investigate a special
parameter regime which has both high anharmonicity ($\sim\!1$GHz) and long
quantum coherence times ($T_1\!=\!40\!-\!80\,\mathrm{\mu s}$ and
$T_\mathrm{2Echo}\!=\!2T_1$).
