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In this paper, we propose an Efficient single-model Variable-bit-rate Codec (EVC), which is able to run at 30 FPS with 768x512 input images and still outperforms VVC for the RD performance. By further reducing both encoder and decoder complexities, our small model even achieves 30 FPS with 1920x1080 input images. To bridge the performance gap between our different capacities models, we meticulously design the mask decay, which transforms the large model's parameters into the small model automatically. And a novel sparsity regularization loss is proposed to mitigate shortcomings of $L_p$ regularization. Our algorithm significantly narrows the performance gap by 50% and 30% for our medium and small models, respectively. At last, we advocate the scalable encoder for neural image compression. The encoding complexity is dynamic to meet different latency requirements. We propose decaying the large encoder multiple times to reduce the residual representation progressively. 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