Detailed structural and functional characterization of proteins by solution NMR requires sequence-specific resonance assignment. We present a set of transverse relaxation optimization (TROSY) based four-dimensional automated projection spectroscopy (APSY) experiments which are designed for resonance assignments of proteins with a size up to 40 kDa, namely HNCACO, HNCOCA, HNCACB and HN(CO)CACB. These higher-dimensional experiments include several sensitivity-optimizing features such as multiple quantum parallel evolution in a 'just-in-time' manner, aliased off-resonance evolution, evolution-time optimized APSY acquisition, selective water-handling and TROSY. The experiments were acquired within the concept of APSY, but they can also be used within the framework of sparsely sampled experiments. The multidimensional peak lists derived with APSY provided chemical shifts with an approximately 20 times higher precision than conventional methods usually do, and allowed the assignment of 90 % of the backbone resonances of the perdeuterated primase-polymerase ORF904, which contains 331 amino acid residues and has a molecular weight of 38.4 kDa.