Setchain has been proposed to increase blockchain scalability by relaxing the strict total order requirement among transactions. Setchain organizes elements into a sequence of sets, referred to as epochs, so that elements within each epoch are unordered. In this paper, we propose and evaluate three distinct Setchain algorithms, that leverage an underlying block-based ledger. Vanilla is a basic implementation that serves as a reference point. Compresschain aggregates elements into batches, and compresses these batches before appending them as epochs in the ledger. Hashchain converts batches into fixed-length hashes which are appended as epochs in the ledger. This requires Hashchain to use a distributed service to obtain the batch contents from its hash. To allow light clients to safely interact with only one server, the proposed algorithms maintain, as part of the Setchain, proofs for the epochs. An epoch-proof is the hash of the epoch, cryptographically signed by a server. A client can verify the correctness of an epoch with $f+1$ epoch-proofs (where $f$ is the maximum number of Byzantine servers assumed). All three Setchain algorithms are implemented on top of the CometBFT blockchain application platform. We conducted performance evaluations across various configurations, using clusters of four, seven, and ten servers. Our results show that the Setchain algorithms reach orders of magnitude higher throughput than the underlying blockchain, and achieve finality with latency below 4 seconds.