Let A and B be nonnegative operators in \({\mathbf {B}}({\mathfrak E})\) , where \({\mathfrak E}\) is a Hilbert space. It will be shown that Ando’s Lebesgue-type decompositions of B with respect to A into a sum \(B=B_1+B_2\) of nonnegative operators \(B_1\) and \(B_2\) , such that \(B_1\) is “absolutely continuous” and \(B_2\) is “singular” with respect to A, can be parametrized with a certain subclass of nonnegative contractions. Moreover, it will be shown that the components \(B_1\) and \(B_2\) in Ando’s Lebesgue-type decompositions need not be mutually singular and the case of their mutual singularity will be characterized. The main idea in the paper is the use of so-called representing maps for the pair of bounded nonnegative quadratic forms associated with A and B. This approach leads also to a construction of the analog of Radon-Nikodym derivative in this setting of Ando.