We compare two tradable permit markets in their ability to meet a safety first environmental target at least cost when some polluters have stochastic, correlated, and non-measurable emissions. In both markets, the point source permit defines the allowable level of the observed (deterministic) point source pollution load. The permit for unobservable and stochastic nonpoint source pollution cannot be defined in this way. One market bases the nonpoint permit on expected nonpoint pollution and uses a trading ratio between the two pollution types to manage stochasticity. This model follows existing point-nonpoint markets for water quality trading. The second model defines the nonpoint permit as a multi-attribute good, where the attributes inform the market about the stochasticity of the underlying pollution load. The multi-attribute permit market is demonstrated to out-perform the trading ratio market. This result is an artifact of polluters directly pricing stochasticity in the former market but not in the latter, where stochasticity is only controllable under highly restrictive conditions.