Large Language Models (LLMs) have been revolutionizing a myriad of natural language processing tasks with their diverse zero-shot capabilities. Indeed, existing work has shown that LLMs can be used to great effect for many tasks, such as information retrieval (IR), and passage ranking. However, current state-of-the-art results heavily lean on the capabilities of the LLM being used. Currently, proprietary, and very large LLMs such as GPT-4 are the highest performing passage re-rankers. Hence, users without the resources to leverage top of the line LLMs, or ones that are closed source, are at a disadvantage. In this paper, we investigate the use of a pre-filtering step before passage re-ranking in IR. Our experiments show that by using a small number of human generated relevance scores, coupled with LLM relevance scoring, it is effectively possible to filter out irrelevant passages before re-ranking. Our experiments also show that this pre-filtering then allows the LLM to perform significantly better at the re-ranking task. Indeed, our results show that smaller models such as Mixtral can become competitive with much larger proprietary models (e.g., ChatGPT and GPT-4).