Conversational search is a difficult task as it aims at retrieving documents based not only on the current user query but also on the full conversation history. Most of the previous methods have focused on a multi-stage ranking approach relying on query reformulation, a critical intermediate step that might lead to a sub-optimal retrieval. Other approaches have tried to use a fully neural IR first-stage, but are either zero-shot or rely on full learning-to-rank based on a dataset with pseudo-labels. In this work, leveraging the CANARD dataset, we propose an innovative lightweight learning technique to train a first-stage ranker based on SPLADE. By relying on SPLADE sparse representations, we show that, when combined with a second-stage ranker based on T5Mono, the results are competitive on the TREC