The focal point of the revealed preference (RP) valuation literature, including recreation demand and random utility maximization (RUM) models, has been on eliciting the "use" value associated with environmental amenities; i.e., that portion of value associated with direct use of a resource. Maler's (1974) concept of weak complementarity is typically invoked to justify this focus. Indeed, weak complementarity explicitly or implicitly underlies most of the RP literature. In this paper, we consider the measurement of welfare in RP models when weak complementarity does not hold. In particular, the Kuhn-Tucker (KT) framework (e.g., Phaneuf et al. 2000) does not impose weak complementarity a priori, raising the possibility of rejecting weakly complementary in estimation and the question as to what is the proper welfare measure to report. Although existence value cannot be measured, we argue that in some circumstances there are components of total value outside of use value onto which RP methods may be able to shed light.