The problem of how SC~~UILIS str~~cr~re affects the extent to which personality factors “determine” a response is probably central to any behavior theory attempting to incerrelace stimulus ambiguity, perception, apperception, and motivational states. Stimulus ambiguity has been studied in relation to many variables: perceptual judgment (Thrasher, 1954), social pressures (Schonbar, 1945), personality integration (Edgar & Shneidman, 1958; Rubinscein, 19541, and identification with the protagonist in TAT-like materials (McIncyre, 1954). This research’ concerns the relation berween graded sti~nulus ambiguity and fantasy production. It was designed in an effort to clarify conflicting reports about rhe relation of the two variables. Efforts to answer the following questions have been of pivotal irnporcance to projective cest theory: (a) Is there an optimal amount of pictorial ambiguity for maximal fantasy excitation? (b) Is the relation between stimulus ambiguity and fantasy arousal linear or non-linear? If non-li near, is it monotonic or non-monoconic? ( c ) Are scimulus ambiguities created by performing different operations functionally equivalent with regard to fantasy-evoking potential? The answers to these questions would be of clearcut value to originators of projective rests and projective play materials. Traditionally researchers used two degrees of stimulus structure rather than ambiguity gradients (Phillips, 1945; Pincler, 1946; Weisskopf, 1950; Proud, 1956). Since two points create the illusion of a straight line when no account is made of the magnitude of the interval between them, historically the implication of linearity becween the two terms, ambiguicy and fantasy, emerged. The issue was sltbsequently reduced co whether there is a direct or inverse relationship between the latter two terms. Thus, 12 years ago Weisskopf ( 1950), using her Transcendence Index as a measure of projected fantasy, found chat a standard TAT card has greater fantasy provoking powers than that card when it is reproduced as an ambiguous variation. However, beginning with the reported findings of Bijou and Kenny (1951) that there is a non-monotonic relationship between stirnul~~s ambiguity and fantasy production, interest has focused on this topic (Kenny, 1954; Kenny & Bijou, 1953; Murstein, 1958). However, the lacer researchers have worked essentially with the concept of response ratherĀ