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The Gravity Recovery and Climate Experiment (GRACE) satellites have measured anomalies in the Earth's time-variable gravity field since 2002, allowing for the measurement of the melting of glaciers due to climate change. Many techniques used with GRACE data have difficulty constraining mass change in small regions, such as Iceland, often requiring broad averaging functions in order to capture trends. These techniques also capture data from nearby regions, causing signal leakage. Alternatively, Slepian functions may solve this problem by optimally concentrating data both in the spatial domain (e.g., Iceland) and spectral domain (i.e., the bandwidth of the data). We use synthetic experiments to show that Slepian functions can capture trends over Iceland without meaningful leakage and influence from ice changes in Greenland. We estimate a mass change over Iceland from GRACE data of approximately -9.3 +/- 1.0 Gt/yr between March 2002 and November 2016, with an acceleration of 1.1 +/- 0.5 Gt/yr(2).