Hereditary spastic paraplegia (HSP) is a degenerative disorder of the motor system, defined by progressive weakness and spasticity of the lower limbs. HSP may be inherited as an autosomal dominant (AD), autosomal recessive, or an X-linked trait. AD HSP is genetically heterogeneous, and three loci have been identified so far: SPG3 maps to chromosome 14q, SPG4 to 2p, and SPG4a to 15q. We have undertaken linkage analysis with 21 uncomplicated AD families to the three AD HSP loci. We report significant linkage for three of our families to the SPG4 locus and exclude several families by multipoint linkage. We used linkage information from several different research teams to evaluate the statistical probability of linkage to the SPG4 locus for uncomplicated AD HSP families and established the critical LOD-score value necessary for confirmation of linkage to the SPG4 locus from Bayesian statistics. In addition, we calculated the empirical P-values for the LOD scores obtained with all families with computer simulation methods. Power to detect significant linkage, as well as type I error probabilities, were evaluated. This combined analytical approach permitted conclusive linkage analyses on small to medium-size families, under the restrictions of genetic heterogeneity.