The limited transparency of the inner decision-making mechanism in deep neural networks (DNN) and other machine learning (ML) models has hindered their application in several domains. In order to tackle this issue, feature attribution methods have been developed to identify the crucial features that heavily influence decisions made by these black box models. However, many feature attribution methods have inherent downsides. For example, one category of feature attribution methods suffers from the artifacts problem, which feeds out-of-distribution masked inputs directly through the classifier that was originally trained on natural data points. Another category of feature attribution method finds explanations by using jointly trained feature selectors and predictors. While avoiding the artifacts problem, this new category suffers from the Encoding Prediction in the Explanation (EPITE) problem, in which the predictor's decisions rely not on the features, but on the masks that selects those features. As a result, the credibility of attribution results is undermined by these downsides. In this research, we introduce the Double-sided Remove and Reconstruct (DoRaR) feature attribution method based on several improvement methods that addresses these issues. By conducting thorough testing on MNIST, CIFAR10 and our own synthetic dataset, we demonstrate that the DoRaR feature attribution method can effectively bypass the above issues and can aid in training a feature selector that outperforms other state-of-the-art feature attribution methods. Our code is available at https://github.com/dxq21/DoRaR.