  We present the first complete model of the Littlest Modular Seesaw, based on
two right-handed neutrinos, within the framework of multiple modular
symmetries, justifying the use of multiple moduli fields which take their
values at 3 specific stabilizers of $\Gamma_4 \simeq S_4$, including a new
phenomenological possibility. Using a semi-analytical approach, we perform a
$\chi^2$ analysis of each case and show that good agreement with neutrino
oscillation data is obtained, including predictive relations between the
leptonic mixing angles and the ratio of light neutrino masses, which
non-trivially agree with the experimental values. It is noteworthy that in this
very predictive setup, the models fit the global fits of the experimental data
remarkably well, both with and without the Super-Kamiokande atmospheric data,
for both choices of stabilizers. By extending the model to include a weighton
and the double cover group $\Gamma'_4 \simeq S'_4$, we are able to also account
for the hierarchy of the charged leptons using modular symmetries, without
altering the neutrino predictions.
