The cut-compliance (CC-) method can be applied in a semi-destructive way by introducing only a shallow slot instead of a cut through the thickness. This requires the influence function to account for the U-shape of the shallow slot and the 3D-effects that affect the stress relaxation. In the present paper a simplified way to evaluate surface stresses from a slot is presented and discussed. By examples it is shown that a two-parameter approximation is often sufficient to characterize the near surface residual stresses in a narrow range of depth. Beyond this range, the procedure described herein can be matched with the common procedure of the CC-method. The analysis is explained first for the simpler case of a 2D-structure. Then the generalization to a 3D-case is shown and discussed. For both cases illustrative examples of measurements are given.