Using a survey of western Canadian agricultural landowners, we examine the cost and viability of two distinct afforestation options for carbon-uptake purposes. Responses to two separate, but most-likely related willingness to accept compensation questions are elicited using the contingent valuation method. Respondents then select the level of certainty with which they believe their responses were given. This paper provides a framework for estimation of the bivariate model with certainty and a modification of the model to incorporate uncertainty based on Li and Mattson's approach to preference uncertainty. While highly preliminary results are given for the bivariate model with certainty, applications of both models will be presented at the 2003 AAEA Meetings.