A plane diagram D of a knot is said to be semi-meandric if D is the union of two simple smooth arcs. Every tame knot has a semi-meandric diagram. We use this fact to define a new knot invariant: the semi-meandric crossing number. Applying the technique of Gauss Codes and a specific algo- rithm transforming arbitrary knot diagrams to semi-meandric ones we obtain estimates on this invariant.