A turbomachine is provided having at least one row of blades oriented at a predetermined stagger. Casing grooves are provided proximate to at least a portion of the tip of the blades. The grooves are oriented substantially normal to the stagger of the blades. The normal of the blade is determined from a chord of the blade. The chord may be taken across a pair of corresponding points one the upstream and downstream end of the blade, hence across the extent of the cross-sectional shape of the blade. Alternatively, a blade chord may be determined over only a portion of the blade, for instance, from a point along the centerline of the upstream end of the blade to a second point on the centerline midway down the blade from the upstream end. Optimally, the grooves are positioned adjacent to the upstream half of the blades, but may continue across the axial extent of the blades. The spacing between grooves can be optimized for blade stagger in order to find an optimal number of grooves that concurrently cross the blade. Additionally, obtaining an optimal groove depth for a particular turbomachine requires knowing only the tip clearance gap as groove depth is directly related to the tip clearance. Furthermore, since the groove may be substantially smaller than prior art casing treatments, fluid recirculation is reduced. The blade-normal groove may take a variety of cross-sectional shapes. Optimally, the aft surface of the groove will have less than a 45° incline to the radial at that point.