Abstract: Transaction fee mechanisms (TFMs) allocate scarce block space in blockchains. Prior work focuses on incentive compatibility (IC): honest behavior maximizes the payoff of each strategic player. We introduce rational-harm proofness (RHP), which rules out deviations that harm honest participants without reducing the deviator's utility relative to honest behavior. IC alone does not exclude such costless harm: in a second-price auction, a losing bidder can raise the winner's payment without changing its own payoff. For finite block capacity k, we characterize TFMs satisfying RHP alongside user incentive compatibility (UIC) and miner incentive compatibility (MIC). In the plain model, where a single miner implements the auction, we prove a tight tetrilemma: no TFM simultaneously achieves positive miner revenue, UIC, MIC, and RHP against miner-user coalitions, while any three are jointly achievable. In the MPC-assisted model, where a committee of miners implements the auction using multi-party computation, we construct a randomized TFM with positive miner revenue satisfying UIC, MIC, and RHP against users, miners, and miner-user coalitions containing at most k users. Randomness is necessary to confirm transactions under congestion: any deterministic TFM satisfying UIC and user RHP in this model confirms no transactions when the number of submitted bids exceeds k. Finally, IC and RHP are incomparable for every strategic role in both models: mechanisms can satisfy either property without satisfying the other. These results extend transaction fee mechanism design beyond incentives to protection against costless harm.