The colossal magnetoresistive manganite La1.2Sr1.8Mn2O7 has been investigated using the 2D-ACAR method in order to obtain information about the Fermi surface. Conventional data analysis methods have been found to yield Fermi-surface topologies which significantly disagree with the size and shape obtained from theoretical bandstructure calculations. We present a method for extracting the Fermi-surface topologies by combining spin-dependent 2D-ACAR measurements with Maximum-Likelihood fitting.