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I have created a transaction with high miner's fee and it is now in mempool (in testnet):
However, it doesn't seem to be confirming. It's already missed two opportunities to confirm. Transactions with much lower miner's fees are going through instead.
Is Bitcoin this random or am I missing something?

Another possible cause is that your transaction has an output which is dust, as do several of its ancestors (which are also still unconfirmed). But I am not sure whether the dust rule is enforced by testnet nodes by default.
– Nate Eldredge – 2018-08-31T04:50:00.620It's confirmed now. – Nate Eldredge – 2018-08-31T13:41:45.797