Interplanetary scintillation (IPS) observations are used to investigate the distribution of microscale density fluctuations in high-speed solar wind streams. A new technique for estimating the electron density power spectrum which can be applied when the solar wind is grossly inhomogeneous is presented. This technique requires accurate knowledge of the radio source structure, in situ measurements of the solar wind velocity, and well-calibrated IPS observations. The estimation algorithm is applied to data obtained during 1973 and 1974 when the solar wind was dominated by recurrent fast streams. It is found that the spectrum has a power law exponent &agr;≈3.2 in the decreasing and low-velocity regions of streams. The spectrum steepens and its level increases in the regions of enhanced density which precede such streams, and it remains steep into the high-velocity regions. The average exponent in these regions is &agr;≈4.1. The average density spectrum obtained from this analysis is consistent with estimates of the spectrum obtained via other techniques.