  We analyze the charge-noise induced coherence time $T_2$ of the fluxonium
qubit as a function of the number of array junctions in the device, $N$. The
pure dephasing rate decreases with $N$, but we find that the relaxation rate
increases, so $T_2$ achieves an optimum as a function of $N$. This optimum can
be much smaller than the number typically chosen in experiments, yielding a
route to improved fluxonium coherence and simplified device fabrication at the
same time.
