Structurally degenerative diseases, such as keratoconus, can significantly alter the stiffness of the cornea, directly affecting the quality of vision. Ultraviolet-induced collagen cross-linking (CXL) effectively increases corneal stiffness and is applied clinically to treat keratoconus. However, measured corneal stiffness is also influenced by intraocular pressure (IOP). Therefore, experimentally measured changes in corneal stiffness may be attributable to the effects of CXL, changes in IOP, or both. We present a noninvasive measurement method using phase-stabilized swept-source optical coherence elastography to distinguish between CXL and IOP effects on measured corneal stiffness. This method compared the displacement amplitude attenuation of a focused air-pulse-induced elastic wave. The damping speed of the displacement amplitudes at each measurement position along the wave propagation were compared for different materials. This method was initially tested on gelatin and agar phantoms of the same stiffness for validation. Consequently, untreated and CXL-treated porcine corneas of the same measured stiffness, but at different IOPs, were also evaluated. The results suggest that this noninvasive method may have the potential to detect the early stages of ocular diseases such as keratoconus or may be applied during CLX procedures by factoring in the effects of IOP on the measured corneal stiffness.