Several stochastic model predictive control schemes are formulated to reduce constraint violations in the economic control of the climate in a lettuce greenhouse under weather forecast and parameter uncertainty. The schemes are tested in simulation. Two separate approaches are taken in the formulations. The first involves analytical constraint tightening through system linearization. Linearizing the system around the trajectory is found to improve performance compared to linearizing around a point. The linearized schemes proved to be overly conservative, especially under parameter uncertainty. The second approach is through tracking the average constraint violations to formulate adaptive constraints which do not require prior information about the underlying uncertainties. Originally proposed for linear systems, this approach is simplified and modified to impose a constraint tightening on deterministic nonlinear model predictive control. The adaptive schemes improve constraint compliance with reduced conservatism leading to a more acceptable increase in input costs compared to the linearized schemes. The results indicate that adaptive average violation constraints may be a useful tool in stochastic model predictive control and warrant further investigation.