Using a large set of ultrasound features does not necessarily ensure improved quantitative classification of breast tumors; rather, it often degrades the performance of a classifier. In this paper, we propose an effective feature reduction approach in the transform domain for improved multi-class classification of breast tumors. Feature transformation methods, such as empirical mode decomposition (EMD) and discrete wavelet transform (DWT), followed by a filter- or wrapper-based subset selection scheme are used to extract a set of non-redundant and more potential transform domain features through decorrelation of an optimally ordered sequence of N ultrasonic bi-modal (i.e., quantitative ultrasound and elastography) features. The proposed transform domain bi-modal reduced feature set with different conventional classifiers will classify 201 breast tumors into benign-malignant as well as BI-RADS⩽3, 4, and 5 categories. For the latter case, an inadmissible error probability is defined for the subset selection using a wrapper/filter. The classifiers use train truth from histopathology/cytology for binary (i.e., benign-malignant) separation of tumors and then bi-modal BI-RADS scores from the radiologists for separating malignant tumors into BI-RADS category 4 and 5. A comparative performance analysis of several widely used conventional classifiers is also presented to assess their efficacy for the proposed transform domain reduced feature set for classification of breast tumors. The results show that our transform domain bimodal reduced feature set achieves improvement of 5.35%, 3.45%, and 3.98%, respectively, in sensitivity, specificity, and accuracy as compared to that of the original domain optimal feature set for benign-malignant classification of breast tumors. In quantitative classification of breast tumors into BI-RADS categories⩽3, 4, and 5, the proposed transform domain reduced feature set attains improvement of 3.49%, 9.07%, and 3.06%, respectively, in likelihood of malignancy and 4.48% in inadmissible error probability compared to that of the original domain optimal subset. In summary, the construction of a transform domain reduced feature set by extracting complementary information from a large set of available bi-modal features and use of qualitative bi-modal BI-RADS can contribute to improved quantitative classification of breast tumors and thereby help reduce the number of unnecessary biopsies, securing a nearly minimum chance of a life-endangering diagnosis.