A medical procedure for use in connection with a patient suffering from cuff tear arthropathy is disclosed. The medial procedure includes providing a humeral prosthesis having a prosthetic head component, wherein (i) the prosthetic head component includes a glenoid-bearing portion and an acromion-bearing portion, and (ii) the glenoid-bearing portion and the acromion-bearing portion define an outer bearing surface, and (iii) the outer bearing surface extends in a medial/lateral direction across a radial distance D, and (iii) D.gtoreq.190.degree.. The medical procedure further includes implanting the humeral prosthesis in the patient so that the acromion-bearing portion contacts and bears directly against a natural acromion of the patient during abduction of an arm of the patient that possesses the humerus.