The magnetic domain structure of ultrathin Co-microstructures on Cu(001) has been investigated by means of a scanning electron microscope with polarization analysis. In particular, the influence of a magnetic field on the domain structure has been studied. Here, we concentrate on squares of different size (3?x2013;30 μm) and variable thickness, although triangles and bars with aspect ratios up to 1:30 have been studied, too. In the as-grown state the microstructures with an edge length larger than 3 μ m exhibit a multidomain structure, while the smaller ones are always single domain. After saturating the structures by a strong field, the magnetization can be switched homogeneously by either ±90^° or 180^° independent of size and shape. The microstructures remain in a single-domain state. Roughly 20% of the ultrathin particles show a two-step 180^°-switching via a 90^°-state. An analytical model is developed yielding coercivities of the right order of magnitude. The two-step reversal process can be explained in the framework of this model.