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The Bitcoin mempool plays an integral role in transaction processing and propagation through the network. Frequent transaction congestion events, as well as spam and dust attacks can clog the mempool, leading to dropped transactions, processing delays, and increased transaction fees. Moreover, increasing transaction loads on the network result in higher resource costs to operate full nodes, thereby restricting Bitcoin's network footprint and negatively impacting its overall health and performance. In this paper, we present Carbyne, a novel mempool optimization scheme, which uses counting bloom filter constructions to adapt to increased transaction flows, thereby making nodes resilient to congestion and spam and dust attacks. We implement Carbyne in C++ and benchmark its performance using a novel data set of Bitcoin mempool activity over a 90-day period. We dramatically reduced the mempool's memory consumption by up to two orders of magnitude (from 300 MB to 3 MB) while verifying and forwarding transactions with 99.9% fidelity and a slight increase in computational load. We simulate extensive spam attacks on Carbyne and demonstrate that mempool loads of 1 GB can be accommodated in as little as 10 MB. Carbyne does not necessitate a hard fork, it will help deploy high-functioning nodes on resource-constrained platforms, and it may also be adapted to other cryptocurrencies.