Large Language Models (LLMs) have become central components of modern applications, yet they remain limited by the context window. The attention mechanism has quadratic complexity in the sequence length and, even when the nominal window is large, models tend not to use all the available information effectively, exhibiting phenomena such as lost in the middle, context rot, and attention collapse. This work investigates non-invasive strategies for context extension, applicable to models accessed through an API without retraining, and proposes a framework that formulates prompt compression as a budget allocation problem. Building on a systematic review of existing techniques and an empirical evaluation of five strategies on long-context benchmarks, compressor selection is formalized as a multiple-choice knapsack problem (MCKP), in which, for each prompt partition, the compression option that maximizes the preserved information is selected under an effective context budget. A screening stage compares four compressors (LLMLingua-GPT2, LLMLingua-2, Selective Context, and a CPC-MiniLM approximation) across five models and two context budgets. CPC-MiniLM achieved the highest average among the four compressors in eight of the ten evaluated combinations, whereas LLMLingua-2 led in both combinations with Qwen 3 30B-A3B. On Gemma 4 26B with 32,768 tokens, CPC-MiniLM reached 0.573, the highest average among the nine compared techniques. These results support the selection of CPC-MiniLM, LLMLingua-2, and Selective Context as MCKP options, whose complete evaluation is presented as a reproducible experimental plan.