A preliminary examination of the tails of 11 Solar and Heliospheric Observatory (SOHO) sungrazers, observed between 3 and 20 R☉ on their approach to the Sun, provides information on dust ejected from these comets and on the forces to which the microscopic grains are subjected. Images taken at times of the SOHO spacecraft's transit across the orbit planes of sungrazers show their tails to be perfectly straight and extremely narrow and their apparent position coinciding with that of the projected orbit plane. This result suggests relatively low particle-ejection velocities in the direction normal to the orbit plane (estimated at less than ~100 m s-1) and offers no evidence whatsoever for the Lorentz force on charged dust. When viewed broadside, the sungrazers' tails are always narrow, either straight or slightly curved, and deviating strikingly from the antisolar direction, an indication that no microscopic dust was ejected during a period of time just preceding observation. The tails include a major population of submicron-sized grains that are dielectric in nature, most probably silicates, since the radiation-pressure accelerations are found never to exceed 0.6 of the solar attraction. The sampled comets show rather consistently that the production of this dust terminated at ~20-30 R☉ from the Sun along the inbound orbit. The tail of one of the brightest SOHO sungrazers is modeled in slightly greater detail, including its curvature, which abruptly increases at a point approximately halfway between the head and the far end.