A proposed solution involves adding the largest non-bucketed UTXO as an additional input during transaction creation to facilitate the refilling process. This strategy aims to generate change outputs that can replenish one or more target buckets by setting a minimum change output size that would adequately refill the most depleted bucket. The approach suggests multiple attempts to create liquidity transactions that include various combinations of missing amounts from the buckets, aiming to find a configuration that minimizes the need for additional change.

The conversation also delves into the technical aspects of how such a system might optimize coin selection for this scenario. It questions the applicability of pre and post-processing steps in coin selection, suggesting an emphasis on the minimum change output size parameter. Given varying fee rates, it recommends creating different types of outputs (P2WPKH and P2TR) depending on whether the focus is on generating bucketed or non-bucketed change outputs. Additionally, the email discusses the potential use of specific coin selection algorithms like CoinGrinder and branch-and-bound (BnB), highlighting their suitability over others like Knapsack and SRD for reducing transaction fees. The possibility of modifying the sendmany RPC call to restrict coin selection to these preferred algorithms is mentioned as a way to streamline the process.

The intricacies of distinguishing between bucketed and non-bucketed UTXOs are considered, pondering whether they should be segregated within separate wallets, amount ranges, or marked distinctly to facilitate the proposed strategy. Concerns about oversplitting, where UTXOs might be divided more than necessary and potentially lead to increased recombination issues later, were raised as a point of caution in refining the strategy.

Finally, the potential applications of this methodology beyond its immediate context are contemplated. While the technique mirrors practices in send-only exchange wallets, which benefit from batching withdrawals into single transactions, it could also serve users engaged in coin join operations, indicating a broader relevance of the proposed solutions for managing UTXOs efficiently while minimizing on-chain fees. The inclusion of a link to the CoinGrinder GitHub repository provides a resource for further exploration of one of the coin selection algorithms recommended for addressing the discussed challenges.