  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. 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 ~ 1.85, possibly
indicating the relevance of second-order Fermi acceleration.
