The extragalactic background light (EBL) is the second-most-intense form of cosmic background light (the first being the cosmic microwave background) and contains the redshifted optical radi- ation, from infra-red to ultraviolet, emitted across all epochs, making it of great cosmological in- terest. While direct measurements of the EBL are hampered by foreground contamination, obser- vations of VHE emission from distant sources can be used to obtain indirect measurements of the EBL. In this work a maximum-likelihood fit is applied to the energy spectra of blazars observed by VERITAS, an array of ground-based imaging atmospheric Cherenkov telescopes sensitive to very-high-energy (VHE; E>100 GeV) gamma rays. Using theoretical models of the EBL shape and intensity, the EBL normalization is treated as a free parameter, allowing for model-dependent constraints to be obtained. Details of this maximum-likelihood analysis and preliminary model- dependent constraints on the EBL, are presented.