  In direct dark matter detection experiments, conventional elastic scattering
of WIMPs results in exponentially falling recoil spectra. In contrast, theories
of WIMPs with excited states can lead to nuclear recoil spectra that peak at
finite recoil energies E_R. The peaks of such signals are typically fairly
broad, with Delta E_R/E_peak ~ 1. We show that in the presence of dark matter
structures with low velocity dispersion, such as streams or clumps, peaks from
up-scattering can become extremely narrow with FWHM of a few keV only. This
differs dramatically from the conventionally expected WIMP spectrum and would,
once detected, open the possibility to measure the dark matter velocity
structure with a fantastic accuracy. As an intriguing example, we confront the
observed cluster of 3 events near 42 keV from the CRESST commissioning run with
this scenario, and find a wide range of parameters capable for producing such a
peak. We compare the possible signals at other experiments, and find that such
a particle could also give rise to the signal at DAMA, although not from the
same stream. Over some range of parameters a signal would be visible at xenon
experiments. We show that such dark matter peaks are a very clear signal, and
can be easily disentangled from potential backgrounds, both terrestrial or due
to WIMP down-scattering, by an enhanced annual modulation signature in both the
amplitude of the signal and its shape.
