Mining attacks allow attackers to gain an unfair share of the mining reward by deviating from the honest mining strategy in the Bitcoin system. Among the most well-known are block withholding (BWH), fork after withholding (FAW), and selfish mining. In this paper, we propose two new strategies: power adjusting and bribery racing, and introduce two novel mining attacks, Power Adjusting Withholding (PAW) and Bribery Selfish Mining (BSM) adopting the new strategies. Both attacks can increase the reward of attackers. Furthermore, we show PAW can avoid the “miner's dilemma” in BWH attacks. BSM introduces a new “venal miner's dilemma”, which results in all targets (bribes) willing to help the attacker but getting less reward finally. Quantitative analyses and simulations are conducted to verify the effectiveness of our attacks. We propose some countermeasures to mitigate the new attacks, but a practical and efficient solution remains to be an open problem.