1ES 1959+650 is one of the most remarkable high-peaked BL Lacertae objects (HBL). In 2002, it exhibited a TeV {gamma}-ray flare without a similar brightening of the synchrotron component at lower energies. This orphan TeV flare remained a mystery. We present the results of a multifrequency campaign, triggered by the INTEGRAL IBIS detection of 1ES 1959+650. Our data range from the optical to hard X-ray energies, thus covering the synchrotron and inverse-Compton components simultaneously. We observed the source with INTEGRAL, the Swift X-Ray Telescope, and the UV-Optical Telescope, and nearly simultaneously with a ground-based optical telescope. The steep spectral component at X-ray energies is most likely due to synchrotron emission, while at soft {gamma}-ray energies the hard spectral index may be interpreted as the onset of the high-energy component of the blazar spectral energy distribution (SED). This is the first clear measurement of a concave X-ray-soft {gamma}-ray spectrum for an HBL. The SED can be well modeled with a leptonic synchrotron self-Compton model. When the SED is fitted this model requires a very hard electron spectral index of q {approx} 1.85, possibly indicating the relevance of second-order Fermi acceleration.