Blockchain systems are designed to produce blocks at a constant average rate. The most popular systems currently employ a Proof of Work (PoW) algorithm as a means of creating these blocks. Bitcoin produces, on average, one block every 10 minutes. An unfortunate limitation of all deployed PoW blockchain systems is that the time between blocks has high variance. For example, 5% of the time, Bitcoin's inter-block time is at least 40 minutes. This variance impedes the consistent flow of validated transactions through the system. We propose an alternative process for PoW-based block discovery that results in an inter-block time with significantly lower variance. Our algorithm, called Bobtail, generalizes the current algorithm by comparing the mean of the k lowest order statistics to a target. We show that the variance of inter-block times decreases as k increases. If our approach were applied to Bitcoin, about 80% of blocks would be found within 7 to 12 minutes, and nearly every block would be found within 5 to 18 minutes; the average inter-block time would remain at 10 minutes. Further, we show that low-variance mining significantly thwarts doublespend and selfish mining attacks. For Bitcoin and Ethereum currently (k=1), an attacker with 40% of the mining power will succeed with 30% probability when the merchant sets up an embargo of 8 blocks; however, when k>=20, the probability of success falls to less than 1%. Similarly, for Bitcoin and Ethereum currently, a selfish miner with 40% of the mining power will claim about 66% of blocks; however, when k>=5, the same miner will find that selfish mining is less successful than honest mining. The cost of our approach is a larger block header.