The DEtection TRansformer (DETR) is a powerful end-to-end object detector, yet its one-to-one matching strategy suffers from slow convergence and low recall. A common approach to address this issue is to use one-to-many label assignment to provide more positive samples. However, existing methods that use one-to-many matching as an auxiliary objective lead to increased training costs, with their auxiliary decoders discarded during inference. To address this limitation, we propose MDS-DETR, which leverages both one-to-one and one-to-many supervision within a single decoder. Specifically, we introduce a Masked Duplicate Suppressor (MDS) that injects asymmetry into self-attention via confidence-based causal masking. MDS filters out the duplicates generated by the one-to-many supervised layer, enables explainable, duplicate-free predictions in a fully end-to-end framework. MDS-DETR outperforms existing one-to-many DETR variants such as MS-DETR, MR.DETR and Relation-DETR, without relying on any additional queries or auxiliary decoders. Under a 12-epoch training schedule on MS COCO with a ResNet-50 backbone, MDS-DETR achieves a +2.8 mAP improvement over Deformable-DETR with only a 5\% increase in training time, and outperforms the state-of-the-art MR.DETR by +0.3 mAP while being even 20\% faster in training. Our code and models are available at \href{https://github.com/dcholee/mds-detr}{https://github.com/DChoLee/MDS-DETR}.