To maximise the economic benefits of tradable emission permits or emission taxes, while keeping these emission pricing mechanisms politically acceptable, requires the use of payment thresholds. There is no other way to avoid the "rock versus hard place" dilemma posed by the standard, polar forms of these pricing mechanisms that are generally discussed by economists, namely auctioned permits, free permits, or a pure tax. This means that in total, the government should auction permits only beyond some payment threshold, and should levy a tax on emissions only beyond a similar threshold. For full symmetry, the latter would mean treating emission taxes like tradable emission permits, with the tax threshold thus a de facto property right, though thresholds less like property rights can still be useful. The importance of a payment threshold is shown empirically for the case of global greenhouse gas abatement, where we use emission pricing to maximise welfare subject to a political constraint on the total control and revenue costs directly paid by emitters. This shows how using a payment threshold allows abatement to be much higher, and welfare to be higher, than with the standard forms of emission pricing.