The results of Phase I of the Princeton-NRAO pulsar survey, carried out at 390 MHz using the 92 m telescope at Green Bank, West Virginia, are presented. This search discovered 34 new pulsars and detected 49 previously known ones. As has been the case with all previous surveys, no pulsars with intrinsic luminosities less than 0.3 mJy/sq kpc have been found. Because of the high sensitivity of the survey and its coverage of nearly 2 sr of sky, the present results imply that such low-luminosity pulsars do not constitute a large portion of the total active pulsar population in the Galaxy. Also in common with previous surveys, the sensitivity of this one deteriorates rather quickly for pulse periods less than a few tenths of a second. The extent to which this loss of sensitivity has biased the period distribution of known pulsars is discussed. 14 references.