The present invention relates firstly to a method for acquiring a stack of microscopic images of a specimen. The microscopic images of the stack are acquired from different focus positions. According to the invention, a plurality of the microscopic images of the specimen are respectively acquired from at least some of the focus positions using different settings of an illumination unit for illuminating the specimen. According to the invention, the illumination settings with which the microscopic images of the specimen are acquired is decided upon individually in each case at least for several of the focus positions. The invention further relates to a digital microscope for microimaging a specimen.