We present frequency distributions of several hard X-ray flare parameters, including peak electron energy injection rate, duration, energy, and X-ray spectral index obtained for several thousand solar hard X-ray flares observed by the ISEE 3/ICE X-ray spectrometer from 1978 to 1986. The sensitivity of this study is approximately 4 photons cm-2 s-1 for photons with energies greater than 30 keV.Above the instrumental threshold, the distributions of flare size and duration can be characterized at all times by power laws, and then the results are comparable to those obtained with SMM, OSO 7, and balloons. Although the power-law indices of the size distributions are constant on a timescale greater than 2 yr, the indices are not constant on shorter timescales. At times when hard X-ray flare activity has minima on a timescale of about 1 month, and most significantly, during the minimum phases of the 154 day periodicity, the frequency distribution is significantly steeper than the nominal distribution. The distributions for peak rate of injected electron energy (or power), duration, and total energy are not independent. When two parameters are correlated, we can define a one-parameter relationship between the slopes of the frequency distributions of the two parameters. Despite the significant change with time in the frequency distributions for most parameters, the relationships between parameters tend to be constant. There is a particularly strong and consistent correlation that suggests that the product of peak electron power times e-folding time is proportional to the total energy. The distribution of spectral index for peak spectra has a mean that is consistent with SMM results. The mean index of the spectra accumulated over the flares' full durations and over the e-folding times is softer. There is a lower limit of approximately 2 on spectral hardness for all but the smallest flares, in agreement with results obtained in an earlier study of OGO 5 data. The observed distributions of spectral index do not change significantly as a function of time. We discuss implications of these observations with regard to solar flare models.