The Reuven Ramaty High Energy Solar Spectroscopic Imager (RHESSI) is a NASA Small Explorer satellite designed to study hard x-ray and gamma-ray emission from solar flares. However, its high-resolution germanium detectors also enable observations of high-energy sources throughout the Universe. This paper discusses the algorithms used to extract spectra, lightcurves, and other information about cosmic gamma-ray bursts, pulsars, and other astrophysical phenomena using an unpointed, spinning array of detectors. Preliminary results and future analysis plans are presented. All RHESSI data are public, and scientists interested in participating should contact the principal author. RHESSI was launched on February 5, 2002, and is a NASA Small Explorer mission built at the University of California, Berkeley, the NASA Goddard Space Flight Center, the Paul Scherrer Institut in Switzerland, and Spectrum Astro, Inc. Its primary science goals are imaging spectroscopy and high-resolution nuclear spectroscopy of solar flares. The instrument consists of 9 large, coaxial germanium detectors that cover an energy range of 3 keV to 17 MeV. Each detector is a closed-end coaxial cylinder with a volume of over 300 cm³, electronically segmented into a thin front segment and a thick rear segment. The front segments shield the rear segments from solar photons below 100 keV and view the Sun through beryllium windows and a small amount of insulating blanket, giving them a useful energy range down to about 3 keV. The rear segments are used for most non-solar observations and have an energy resolution of about 4 keV FWHM at 2 MeV when summed together. RHESSI data are telemetered one photon at a time with full energy and time resolution. A variety of analyses are possible on the same dataset without the restrictions usually encountered by having to put an instrument into "burst mode", "pulsar mode", etc. The possible non-solar observations fall into four categories based on the technique used to distinguish between source and background counts: observations of burst emission, imaged observations, observations of pulsed emission, and observations using occultation of the source. RHESSI has been used to study cosmic gamma-ray bursts (GRBs) and bursts from Soft Gamma Repeaters (SGRs). The data from RHESSI have been used to help create or refine several IPN error boxes. RHESSI can also provide a crude position measurement for a burst by itself. As the satellite rotates at 15 rpm, the nine germanium detectors occult each other, so that a GRB coming in from the side is modulated. The azimuth angle can be obtained from the phase of the modulation. For a burst of <<4 s, simple count ratios in the different rear segments can be used and compared to models for different azimuthal angles. The polar angleThe Reuven Ramaty High Energy Solar Spectroscopic Imager (RHESSI) is a NASA Small Explorer satellite designed to study hard x-ray and gamma-ray emission from solar flares. However, its high-resolution germanium detectors also enable observations of high-energy sources throughout the Universe. This paper discusses the algorithms used to extract spectra, lightcurves, and other information about cosmic gamma-ray bursts, pulsars, and other astrophysical phenomena using an unpointed, spinning array of detectors. Preliminary results and future analysis plans are presented. All RHESSI data are public, and scientists interested in participating should contact the principal author. RHESSI was launched on February 5, 2002, and is a NASA Small Explorer mission built at the University of California, Berkeley, the NASA Goddard Space Flight Center, the Paul Scherrer Institut in Switzerland, and Spectrum Astro, Inc. Its primary science goals are imaging spectroscopy and high-resolution nuclear spectroscopy of solar flares. The instrument consists of 9 large, coaxial germanium detectors that cover an energy range of 3 keV to 17 MeV. Each detector is a closed-end coaxial cylinder with a volume of over 300 cm³, electronically segmented into a thin front segment and a thick rear segment. The front segments shield the rear segments from solar photons below 100 keV and view the Sun through beryllium windows and a small amount of insulating blanket, giving them a useful energy range down to about 3 keV. The rear segments are used for most non-solar observations and have an energy resolution of about 4 keV FWHM at 2 MeV when summed together. RHESSI data are telemetered one photon at a time with full energy and time resolution. A variety of analyses are possible on the same dataset without the restrictions usually encountered by having to put an instrument into "burst mode", "pulsar mode", etc. The possible non-solar observations fall into four categories based on the technique used to distinguish between source and background counts: observations of burst emission, imaged observations, observations of pulsed emission, and observations using occultation of the source. RHESSI has been used to study cosmic gamma-ray bursts (GRBs) and bursts from Soft Gamma Repeaters (SGRs). The data from RHESSI have been used to help create or refine several IPN error boxes. RHESSI can also provide a crude position measurement for a burst by itself. As the satellite rotates at 15 rpm, the nine germanium detectors occult each other, so that a GRB coming in from the side is modulated. The azimuth angle can be obtained from the phase of the modulation. For a burst of <<4 s, simple count ratios in the different rear segments can be used and compared to models for different azimuthal angles. The polar angle