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Behavioral cloning (BC) provides a straightforward solution to offline RL by mimicking offline trajectories via supervised learning. Recent advances (Chen et al., 2021; Janner et al., 2021; Emmons et al., 2021) have shown that by conditioning on desired future returns, BC can perform competitively to their value-based counterparts, while enjoying much more simplicity and training stability. While promising, we show that these methods can be unreliable, as their performance may degrade significantly when conditioned on high, out-of-distribution (ood) returns. This is crucial in practice, as we often expect the policy to perform better than the offline dataset by conditioning on an ood value. We show that this unreliability arises from both the suboptimality of training data and model architectures. We propose ConserWeightive Behavioral Cloning (CWBC), a simple and effective method for improving the reliability of conditional BC with two key components: trajectory weighting and conservative regularization. Trajectory weighting upweights the high-return trajectories to reduce the train-test gap for BC methods, while conservative regularizer encourages the policy to stay close to the data distribution for ood conditioning. We study CWBC in the context of RvS (Emmons et al., 2021) and Decision Transformers (Chen et al., 2021), and show that CWBC significantly boosts their performance on various benchmarks.