In this paper, we formulate a new integrity constraint in correlation with 3-valued stable models in an abduction framework based on general logic programs. Under the constraint, not every ground atom or its negation is a logical consequence of the theory and an expected abductive explanation, but some atom may be unspecified as a logical consequence by an adjustment. As a reflection of the integrity constraint with an adjustment, we augment an adjusting derivation to Eshghi and Kowalski abductive proof procedure, in which such an unspecified atom can be dealt with.