We introduce a two-level stochastic capacitated lot-sizing problem with random demand and service level constraints under the static and static-dynamic uncertainty strategy. While the static strategy determines setup periods and lot-sizes at the beginning of the planning horizon, the static-dynamic strategy allows adjustments of lot-sizes during the planning horizon. We present a model formulation of the demand difference adaptation policy for a multi-stage production system. Thereby, lot-size adaptations depend on demand differences between the realized and expected demand. We evaluate 144 test instances with different parameter settings to quantify the economic efficiency of the uncertainty strategies for the multilevel lot-sizing problem. The computational study demonstrates that additional costs of semifinished goods and scarcity of storage capacity on upstream precesses reduce the cost saving potential of lot-size adaptations.