Reliable identification of encrypted file fragments is a requirement for several security applications, including ransomware detection, digital forensics, and traffic analysis. A popular approach consists of estimating high entropy as a proxy for randomness. However, many modern content types (e.g. office documents, media files, etc.) are highly compressed for storage and transmission efficiency. Compression algorithms also output high-entropy data, thus reducing the accuracy of entropy-based encryption detectors. Over the years, a variety of approaches have been proposed to distinguish encrypted file fragments from high-entropy compressed fragments. However, these approaches are typically only evaluated over a few, select data types and fragment sizes, which makes a fair assessment of their practical applicability impossible. This paper aims to close this gap by comparing existing statistical tests on a large, standardized dataset. Our results show that current approaches cannot reliably tell apart encryption and compression, even for large fragment sizes. To address this issue, we design EnCoD, a learning-based classifier which can reliably distinguish compressed and encrypted data, starting with fragments as small as 512 bytes. We evaluate EnCoD against current approaches over a large dataset of different data types, showing that it outperforms current state-of-the-art for most considered fragment sizes and data types.