We have used scanning tunneling microscopy and low-energy electron diffraction to study the preparation of hydrogen-terminated Si(111)1 X 1 surfaces by in situ atomic-hydrogen exposure of Si(111)7 X 7 surfaces. We find that exposure at sample temperatures of 350-480-degrees-C with a hydrogen dose above 1000 L results in the complete transformation of the 7 X 7 structure to the H-terminated 1 X 1 structure. The highest quality Si(111)1 X 1-H surfaces are obtained for doses of 5000 L hydrogen at a temperature around 380-degrees-C. These surfaces have less than 5% of a monolayer stacking faults, approximately 1% point-like defects, and less than 0.5% of contamination. For larger hydrogen doses the amount of stacking faults is further reduced, but the surfaces become rough due to the formation of holes in the first bulk double layer. A discussion of the temperature dependence of the removal of the stacking faults is presented as well as a discussion on the origin of the most frequently occurring point-like defects.