Extreme multi-label (XML) classification refers to the task of supervised multi-label learning that involves a large number of labels. Hence, scalability of the classifier with increasing label dimension is an important consideration. In this paper, we develop a method called LightDXML which modifies the recently developed deep learning based XML framework by using label embeddings instead of feature embedding for negative sampling and iterating cyclically through three major phases: (1) proxy training of label embeddings (2) shortlisting of labels for negative sampling and (3) final classifier training using the negative samples. Consequently, LightDXML also removes the requirement of a re-ranker module, thereby, leading to further savings on time and memory requirements. The proposed method achieves the best of both worlds: while the training time, model size and prediction times are on par or better compared to the tree-based methods, it attains much better prediction accuracy that is on par with the deep learning based methods. Moreover, the proposed approach achieves the best tail-label prediction accuracy over most state-of-the-art XML methods on some of the large datasets\footnote{accepted in IJCNN 2023, partial funding from MAPG grant and IIIT Seed grant at IIIT, Hyderabad, India. Code: \url{https://github.com/misterpawan/LightDXML}