Provided are methods for reducing intraocular pressure in an individual having an ocular disorder causing elevated intraocular pressure, such as glaucoma. The method comprises administering to the individual an effective intraocular pressure-reducing amount of a pharmaceutical composition comprising an A.sub.3 subtype adenosine receptor (A.sub.3AR) antagonist, including dihydropyridine, pyridine, pyridinium salt or triazoloquinazoline, and derivatives thereof expressly having A.sub.3AR antagonist activity, including, e.g., the nucleoside-based A.sub.3AR antagonist, MRS-3820. Further provided is a method for ensuring the delivery of a topically administered therapeutic composition for reducing intraocular pressure, wherein the method expressly requires physically opening a channel through the corneal barrier of the patient's eye by a microneedle or micropipette to permit transport of the topical composition to the anterior chamber of the eye.