A quasi-residual design is defined in [8] as a BIBD having the parameters of a residual design. The main problem concerning these designs lies in answering the question "Is a quasi-residual design necessarily a residual design?" For 2 = 1 or 2 it has been shown that all quasi-residual designs are also residual designs (Connor and Hall [3]), but a counter-example for the design (16, 24, 9, 6, 3) due to Bhattacharya [1], shows this not to be the case for 2=3. The impossibility of the Bhattacharya design being a residual of a corresponding symmetric design (25, 25, 9, 9, 3) rests upon the fact that two blocks in the design intersect in four varieties, whereas any two blocks in a symmetric design have precisely 2 varieties in common. In general, any quasi-residual design which contains a pair of blocks intersecting in more than 2 varieties will not be a residual design. It is interesting to note, however, that the Bhattacharya example seems to be the only presently known design with this property, and that until recently, little else was known concerning quasi-residual designs with 2 > 2. For any block B in a design we define intersection numbers al (i=0, 1, 2, ...) by