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We report on the VERITAS observations of the high-frequency peaked BL Lac object 1ES 1959+650 in the period 2007-2011. This source is detected at TeV energies by VERITAS at 16.4 standard deviation (sigma) significance in 7.6 hr of observation in a low flux state. A multiwavelength spectral energy distribution (SED) is constructed from contemporaneous data from VERITAS, Fermi-LAT, RXTE PCA, and Swift UVOT. Swift XRT data is not included in the SED due to a lack of simultaneous observations with VERITAS. In contrast to the orphan gamma-ray flare exhibited by this source in 2002, the X-ray flux of the source is found to vary by an order of magnitude, while other energy regimes exhibit less variable emission. A quasi-equilibrium synchrotron self-Compton model with an additional external radiation field is used to describe three SEDs corresponding to the lowest, highest, and average X-ray states. The variation in the X-ray spectrum is modeled by changing the electron injection spectral index, with minor adjustments of the kinetic luminosity in electrons. This scenario produces small-scale flux variability of the order of less than or similar to 2 in the high energy (E > 1MeV) and very high energy (E > 100 GeV) gamma-ray regimes, which is corroborated by the Fermi-LAT, VERITAS, and Whipple 10 m telescope light curves.