With context windows of millions of tokens, Long-Context Language Models (LCLMs) can encode entire document collections, offering a strong alternative to conventional retrieval-augmented generation (RAG). However, it remains unclear whether fine-tuning strategies can improve long-context performance and translate to greater robustness under KV-cache compression techniques. In this work, we investigate which training strategies most effectively enhance LCLMs’ ability to identify and use relevant information, as well as enhancing their robustness under KV-cache compression. Our experiments show substantial in-domain improvements, achieving gains of up to +20 points over the base model. However, out-of-domain generalization remains task dependent with large variance – LCLMs excels on finance questions (+9 points), while RAG shows stronger performance on multiple-choice questions (+6 points) over the baseline models. Finally, we show that our fine-tuning approaches bring moderate improvements in robustness under KV-cache compression, with gains varying across tasks.