Public acceptance of environmental compensation (offsetting) as a mechanism to address negative human impacts on biodiversity and ecosystem services is critical. Given that "in-kind/on-site" compensation is rarely possible, proposals must address trade-offs with respect to design. We measure Swedish citizens' support for compensation and analyze preferences for design attributes based on a choice experiment in which respondents choose between various compensation alternatives to address the hypothetical loss of green space due to urban development. We find citizens' support for compensation is high, but the activity causing the damage affects acceptance. Our model suggests that several design attributes affect choice but size of the compensation area was valued highest, both in relative and absolute terms. Further, our results suggest that compensation should be primarily focused on creating or improving biodiversity and nature values in order to be in line with public preferences. Additionally, choice depends on interactions between attributes: a larger compensation site matters more when it is relatively further away; and the importance of size and distance from damage depends on whether compensation type focuses on nature or recreational values. Observable characteristics such as a respondent's age, income and education affect compensation design preferences, but perceptions and previous experiences have the largest effect on choice. Our findings suggest that public preferences are consistent with many of the general recommendations found in guidance documents, but local context may argue for alternative priorities with respect to certain species, habitats, and/or the wellbeing of certain groups. To engender broad support, compensatory offsets will need to balance scientific rigor with transparent involvement of the public.