The concept of creating a "changeless solution" for liquidity transactions by targeting specific amounts that correspond to the deficits in various buckets presents an intriguing approach. This method involves generating multiple target amounts by combining different missing sums and attempting to construct transactions for each separately, maximizing the efficiency of UTXO usage.

The use of bucketed UTXOs is discussed as a potential strategy, albeit with some reservations. Initially, it might seem logical to rely on bucketed UTXOs due to the assumption that most of the wallet's value resides in these categories, apart from a few original funding UTXOs which are larger than the largest bucket. However, this assumption may not hold true in all cases, especially when considering that closing channels can generate UTXOs with random amounts that do not fit neatly into predefined buckets.

An alternative proposition focuses on the scenario where it's impossible to create a funding transaction without change. In such cases, the goal shifts towards creating transactions that minimize leftover change by exactly refilling depleted buckets. This strategy often relies on utilizing the largest non-bucketed UTXO available to replenish the buckets. Over time, this process either results in generating a change output that falls within a bucket or remains between buckets, similar to the outcomes observed when channels are closed. The suggestion hints at the possibility of consolidating UTXOs when transaction fees are low, offering a practical way to manage the inefficiencies associated with UTXO distribution.

In summary, the exploration of strategies to enhance liquidity transaction efficiency underscores the need for flexible and adaptive approaches in managing UTXO allocations. Whether through seeking changeless solutions or optimizing the use of bucketed and non-bucketed UTXOs, the overarching goal remains to streamline transactions while minimizing unnecessary outputs, thereby improving the overall effectiveness of cryptocurrency management practices.