Bitcoin has provided a framework for a decentralized currency system. However, the irregular payouts of its winner-takes-all reward strategy have proven to be unacceptable for the miners who are responsible for verifying transactions. To address this problem, miners have formed mining pools to ensure more regular rewards, but these mining pools undermine the decentralization that is one of Bitcoin’s key benefits. Previous work has sought to make it impossible for mining pools to form, but it is not clear that the situation would improve without addressing the economic incentives that lead to the formation of mining pools in the first place. This work introduces SharedWealth, a protocol designed to reward miners who find “near misses” to the required proof-of-work target to make a Bitcoin block. We show how this approach provides miners with more regular pay, decreasing their incentives to join a mining pool. We use a burn-and-mint strategy, where new rewards are paid out based on the expected number of near misses rather than dividing up the rewards according to the actual number of near misses, thus eliminating any incentive for a block producer to discard the near misses of other miners.