The quality of explanations for the predictions made by complex machine learning predictors is often measured using insertion and deletion metrics, which assess the faithfulness of the explanations, i.e., how accurately the explanations reflect the predictor's behavior. To improve the faithfulness, we propose insertion/deletion metric-aware explanation-based optimization (ID-ExpO), which optimizes differentiable predictors to improve both the insertion and deletion scores of the explanations while maintaining their predictive accuracy. Because the original insertion and deletion metrics are non-differentiable with respect to the explanations and directly unavailable for gradient-based optimization, we extend the metrics so that they are differentiable and use them to formalize insertion and deletion metric-based regularizers. Our experimental results on image and tabular datasets show that the deep neural network-based predictors that are fine-tuned using ID-ExpO enable popular post-hoc explainers to produce more faithful and easier-to-interpret explanations while maintaining high predictive accuracy. The code is available at https://github.com/yuyay/idexpo.