We present two methods to improve the well-known algorithms for hyperspectral point target detection: the constrained energy minimization algorithm (CEM), the Generalized Likelihood Ratio Test algorithm (GLRT) and the adaptive coherence estimator algorithm (ACE). The original algorithms rely solely on spectral information and do not use spatial information; this is normally justified in subpixel target detection since the target size is smaller than the size of a pixel. However, we have 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, we should consider spatial filtering algorithms. The first improvement uses the local spatial mean and covariance matrix which take into account the spatial local mean instead of the global mean. The second considers the fact that the target physical sub-pixel size will appear in a cluster of pixels. We test our algorithms by using the dataset and scoring methodology of the Rochester Institute of Technology (RIT) Target Detection Blind Test project. Results show that both spatial methods independently improve the basic spectral algorithms mentioned above; when used together, the results are even better.