Many geoscientists argue that there is a gravity low of 10-30 mGal in Fennoscandia as a remaining fingerprint of the last ice age and load, both vanished about 10 kyr ago. However, the extraction of the gravity signal related with Glacial Isostatic Adjustment (GIA) is complicated by the fact that the total gravity field is caused by many significant density distributions in the Earth. Here we recall a methodology originating with A. Bjerhammar 35 years ago, that emphasizes that the present land uplift phenomenon mainly occurs in the region thatwas covered by the ice cap, and it is highly correlated with the spectral window of degrees 10-22 of the global gravity field, whose lower limit fairly well corresponds to the wavelength that agrees with the size of the region. This implies that, although in principle the GIA is a global phenomenon, the geoid and gravity lows as well as the land upheaval in Fennoscandia are typically regional phenomena that cannot be seen in a global correlation study as it is blurred by many irrelevant gravity signals. It is suggested that a regional multi-regression analysis with a band-limited spectral gravity signal as the observable, a method tested already 2 decades ago, can absorb possible significant disturbing signals, e.g. from topographic and crustal depth variations, and thereby recover the GIA signal.