As better precision is achieved and more sophisticated reduction methods are created previously invisible biases surface. This has been especially true in astrometric Schmidt plate work. The problem of their amelioration is not fully solved and precision per se is meaningless in the presence of poor accuracy of comparable amplitude. Continuing to benignly neglect this issue puts us in the position of standing on only one statistical leg. New techniques have been designed to further minimize systematic errors. Of especial interest to star catalog analysis is the method of infinitely overlapping circles (Taff, Bucciarelli & Lattanzi, ApJ 361, 667, 1990; Taff, Bucciarelli & Lattanzi, ApJ 392, 746 1992; Bucciarelli, Taff & Lattanzi, J. Stat. Comp. and Sim. 48, 29 1993). With it almost complete success has occurred with regard to the removal of systematic errors which creep into compilation catalogs as a result of inadequate treatment of catalog-to-catalog systematic errors; they can essentially be eliminated a priori or a posteriori (Bucciarelli, Lattanzi & Taff, in press in ApJ 1994; Taff & Bucciarelli, in press in ApJ 1994). What infinitely overlapping circles does can be briefly described as follows: Let X (x) be the measured (true) value of a standard coordinate, S(x,y) (ε) be the systematic (random) error in x at this point, let w∞ be the infinitely overlapping circle weight, a be the standard deviation of the random error in x, N be the total number of stars in this circle which has radius R, and x0,y0 be the coordinates of the center of this circle.