This paper describes a procedure for making short-term predictions by examining trajectories on a reconstructed attractor that correspond to a dynamical feature of interest, namely, the trajectories near a spiral saddle fixed point in the attractor. Reasonable predictions can be made from short time series records and very good predictions from longer records using local linear approximations of the dynamics, if the dimension of the attractor is not too large. Two methods are described. The first uses nearest-neighbor comparisons similar to E. N. Lorenz’ “method of analogues.” The second method uses a collection of closely matched trajectories to compute a basis of singular vectors. The observations can be projected onto a subset of the new basis with little loss of information. In the new coordinates, good predictions can be made by finding the slope of a certain least-squares line through the origin.