Objective: The objective of this study was to assess the conditions under which Zambian women with a history of cervical cancer screening by visual inspection with acetic acid might switch to human papillomavirus-based testing in the future. Materials and Methods: We conducted a choice-based conjoint survey in a sample of women recently screened by visual inspection in Lusaka, Zambia. The screening attribute considered in hypothetical-choice scenarios included screening modality, sex and age of the examiner, whether screening results would be presented visually, distance from home to the clinic, and wait time for results. Results: Of 238 women in the sample, 208 (87.4%) provided responses sufficiently reliable for analysis. Laboratory testing on a urine sample was the preferred screening modality, followed by visual screening, laboratory testing on a self-collected vaginal specimen, and laboratory testing on a nurse-collected cervical specimen. Market simulation suggested that only 39.7% (95% CI = 33.8-45.6) of the respondents would prefer urine testing offered by a female nurse in her 30s over visual inspection of the cervix conducted by a male nurse in his 20s if extra wait time were as short as 1 hour and the option of viewing how their cervix looks like were not available. Conclusions: Our study suggests that, for somewomen, the level of preference for human papillomavirus-based screening strategies may depend highly on the process and conditions of service delivery.