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• This study examines preferences for multiple urban forest structure-function attributes. • We quantify the differences in willingness-to-pay for these attributes across the population. • Findings can inform policy initiatives and provide evidence of preference heterogeneity. The structural and functional attributes of urban and peri-urban forests are the basis for the provision of a suite of ecosystem services that directly and indirectly benefit residents across scales, tenures and land uses. As such, many local governments promote municipal urban forest initiatives such as maintenance and management plans, ordinances, and tree-giveaway programs (e.g. Orlando, USA and Sydney, Australia). However, the effectiveness and distributional fairness of these activities often overlooks residents' values and preferences for certain tree functional traits, sizes, densities and associated costs. This study implements an online survey of 724 Florida, USA residents, to: 1) examine preferences/tradeoffs for multiple urban forest structure-function attributes; 2) quantify and assess the differences in willingness-to-pay (WTP) for these forest structure attributes in public areas; and 3) examine the implications of value heterogeneity for tree function-structure attributes for purposes of crafting policies or designing public programs dealing with urban forests. Only 19% of respondents indicated a serious concern about living close to trees and flowering plants that produce pollen that can result in allergies. Similarly, only 12% were concerned about hurricane wind impacts to and from their treescapes. Using latent class modeling and a stated preferences panel data, our results reveal important differences in WTP along multiple value groups, each with different WTP values for: tree nativity (native vs. exotic); number of species (many vs. few) and size of trees (fully grown vs. mix of ages); as well as maintenance costs. The novel approach of this study indicates the importance of using tree functional traits versus species taxa and accounting for diverse values among the public for more effective decisions. Findings can be used to inform timely policy initiatives, while providing additional evidence of the ubiquity of the public's heterogeneous values and providing guidance to avoid potentially misleading policy interpretations. [ABSTRACT FROM AUTHOR]