Synthetic targeted optimization of plant promoters is becoming a part of progress in mainstream postgenomic agriculture along with hybridization of cultivated plants with wild congeners, as well as marker-assisted breeding. Therefore, here, for the first time, we compiled all the experimental data-on mutational effects in plant proximal promoters on gene expression-that we could find in PubMed. Some of these datasets cast doubt on both the existence and the uniqueness of the sought solution, which could unequivocally estimate effects of proximal promoter mutation on gene expression when plants are grown under various environmental conditions during their development. This means that the inverse problem under study is ill-posed. Furthermore, we found experimental data on in vitro interchangeability of plant and human TATA-binding proteins allowing the application of Tikhonov's regularization, making this problem well-posed. Within these frameworks, we created our Web service Plant_SNP_TATA_Z-tester and then determined the limits of its applicability using those data that cast doubt on both the existence and the uniqueness of the sought solution. We confirmed that the effects (of proximal promoter mutations on gene expression) predicted by Plant_SNP_TATA_Z-tester correlate statistically significantly with all the experimental data under study. Lastly, we exemplified an application of Plant_SNP_TATA_Z-tester to agriculturally valuable mutations in plant promoters.