Gene expression profiles of heterogeneous bulk samples contain signals from multiple cell populations. Studying variations in their composition can help to identify cell populations relevant for disease. Moreover, analyses, such as the identification of differentially expressed genes, can be confounded by cellular composition, as differences in gene expression may arise from both variations in cellular composition and gene regulation. Here, we present Deconvolution of omics data (Deconomix) -- a comprehensive toolbox for the cell-type deconvolution of bulk transcriptomics data. Deconomix stands apart from competing solutions with rich functionality and highly efficient implementations. It facilitates (A) the inference of cellular compositions from bulk transcriptomics data, (B) the machine learning-based optimization of gene weights to resolve small cell populations and to disentangle phenotypically related cells, (C) the inference of background contributions which otherwise would deteriorate cell-type deconvolution, and (D) population estimates of cell-type specific gene regulation. Availability: Deconomix is available at: https://gitlab.gwdg.de/MedBioinf/MedicalDataScience/Deconomix under GPLv3 licensing. The Python package can be easily installed via pip. It comes with a comprehensive documentation of all user-relevant functions and example workflows provided as Jupyter notebooks.