Prompt compression is aimed at reducing input prompt lengths to enable cheaper, faster, and potentially higher-quality LLM predictions. However, existing prompt compression methods are often limited by modest compression gains, a risk of hallucination, and/or high compression latency. We propose EffComp, an **Eff**icient prompt **Comp**ression framework for RAG-based question answering (QA). EffComp employs BERT-style document reranker and sentence selector models to allow fast extractive prompt compression at the sentence level. Its extractive nature prevents hallucinations in the compressed prompts. Additionally, the training process using a hybrid reinforcement and supervised learning approach is designed to optimize the compression ratio while preserving LLM accuracy. Experiments on various QA datasets demonstrate that EffComp outperforms state-of-the-art prompt compression methods achieving the best trade-off between compression ratio and accuracy with minimal latency. This makes it practical for real-world applications.