We present two methods to improve three hyperspectral stochastic algorithms for target detection; the algorithms are the constrained energy minimization, the generalized likelihood ratio test, and the adaptive coherence estimator. The original algorithms rely solely on spectral information and do not use spatial information; this usage is normally justified in subpixel target detection, since the target size is smaller than the size of a pixel. However, we found that since the background (and the false alarms) may be spatially correlated and the point spread function can distribute the energy of a point target between several neighboring pixels, the implementation of spatial filtering algorithms considerably improved target detection. Our first improvement used the local spatial mean and covariance matrices, which take into account the spatial local mean instead of the global mean. While this concept has been found in the literature, the effect of its implementation in both the estimated mean and the covariance matrix is examined quantitatively here. The second was based on the fact that the effect of a target of physical subpixel size will extend to a cluster of pixels. We tested our algorithms by using the data set and scoring methodology of the Rochester Institute of Technology Target Detection Blind Test project. The results showed that both spatial methods independently improved the basic spectral algorithms mentioned above, and when the two methods were used together, the results were even better.