The variance of the North Atlantic Oscillation index (denoted N) is shown to depend on its coupling with area-averaged sea ice concentration anomalies in and around the Barents Sea (index denoted B). The observed form of this coupling is a negative feedback whereby positive N tends to produce negative B, which in turn forces negative N. The effects of this feedback in the system are examined by modifying the feedback in two modeling frameworks: a statistical vector autoregressive model (F (VAR)) and an atmospheric global climate model (F (CAM)) customized so that sea ice anomalies on the lower boundary are stochastic with adjustable sensitivity to the model's evolving N. Experiments show that the variance of N decreases nearly linearly with the sensitivity of B to N, where the sensitivity is a measure of the negative feedback strength. Given that the sea ice concentration field has anomalies, the variance of N goes down as these anomalies become more sensitive to N. If the sea ice concentration anomalies are entirely absent, the variance of N is even smaller than the experiment with the most sensitive anomalies. Quantifying how the variance of N depends on the presence and sensitivity of sea ice anomalies to N has implications for the simulation of N in global climate models. In the physical system, projected changes in sea ice thickness or extent could alter the sensitivity of B to N, impacting the within-season variability and hence predictability of N.