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Many mammal and bird species respond to predator encounters with alarm vocalizations that generate risk-appropriate responses in listeners. Two conceptual frameworks are typically applied to the information encoded in alarm calls and to associated anti-predator behaviors. ‘Functionally referential’ alarm systems encode nominal classes or categories of risk in distinct call types that refer to distinct predation-risk situations. ‘Risk-based’ alarms encode graded or ranked threat-levels by varying the production patterns of the same call types as the urgency of predation threat changes. Recent work suggests that viewing alarm-response interactions as either referential or risk-based may oversimplify how animals use information in decision-making. Specifically, we explore whether graded alarm cues may be useful in classifying risks, supporting a referential decision-making framework. We presented predator (hawk, owl, cat, snake) and control treatments to captive adult tufted titmice Baeolophus bicolor and recorded their vocalizations, which included ‘chick-a-dee’ mobbing calls (composed of chick and D notes), ‘seet’ notes, two types of contact notes (‘chip’, ‘chink’), and song. No single call type was uniquely associated with any treatment and the majority of acoustic measures varied significantly among treatments (46 of 60). The strongest models (ANOVA and classification tree analysis) grouped hawk with cat and owl, and control with snake, and were based on the number or proportion of a) chick and D notes per chick-a-dee call, b) chip versus chink notes produced following treatment exposure, and c) the frequency metrics of other note types. We conclude that (1) the predation-threat information available in complex titmouse alarm calls was largely encoded in graded acoustic measures that were (2) numerous and variable across treatments and (3) could be used singly or in combinations for either ranking or classification of threats. We call attention to the potential use of mixed threat identification strategies, where risk-based signal information may be used in referential decision-making contexts.