This paper generalizes the usual ε-contamination class Γ(π 0 , ε, Q )={π: π=(1−ε)π 0 +εq, for some q∈ Q } . The class considered is Γ(ε 0 , ε 1 ,…,ε m , Q 0 , Q 1 ,…, Q m ) which is defined to be {π: π=ε 0 q 0 +ε 1 q 1 +⋯+ε m q m , for some q 0 ∈ Q 0 , q 1 ∈ Q 1 ,…, q m ∈ Q m } . This class encompasses many of the classes of priors used in Bayesian robustness and sensitivity analyses. Also, by taking Q 0 ⊂ Q 1 ⊂⋯⊂ Q m one can model partial prior information of ‘graded’ precision, i.e.where, with decreasing confidence, one can specify the prior more precisely. One can specify quantiles of the prior, either exactly or within bounds, moments of the prior, shape or smoothness constraints, or that the prior is within neighborhoods (of varying sizes), metric or otherwise, of a base prior. One need not assume an inclusion ordering among the Q i 's, and thus could model conflicting partial prior information with various degrees of prior belief in the information. Extremes of posterior expectations can be determined for this class by using the linearization techniques of Lavine ( J. Amer. Statist. Assoc. 86 (1991) 143–156) and Lavine et al. ( J. Statist. Plann. Inference. to appear).