The operators used for common-reflection-surfaces stack or interpolation are redundant in view of their information. In addition, each operator is usually uniquely used for a target sample. Our aim is to make use of this redundancy in order to gain more information for each target sample. In addition, we reduce the redundancy by distinguishing between the target grid and a coarser parameter grid. Having estimated an operator on the parameter grid, we can use it as stacking or interpolation operator for each sample of the target grid that falls into its range of validity. In this manner each sample of the target grid is alimented with numerous operators. This parameter-oriented scheme has a reliable smoothing effect and overcomes the problem that a single operator estimation for a target sample fails. For the illustration of the method we use the common-reflection-surface interpolation for 2D and apply the target and the parameter-oriented schemes to the Sigsbee data. Although we present the parameter-oriented imaging for the 2D case the scheme applies similar to the 3D case.