Conjoint analysis (CA) is concerned with estimating consumer choice behavior for products and services and/or underlying preference structures as a function of tangible specifications such as the cost of a product and duration of a service. Although constraints influence consumers’ preferences by forcing them to make specific trade-off across attributes, and affect what can be offered to the consumers, they have received little attention in the conjoint analysis literature. Such constraints have implications for CA design and the practicality of discrete attribute levels. This paper discusses the principles underlying mixture amount designs and compares the approach to the traditional fractional factorial designs in examples of travel time allocation to four different activities subject to time constraints of individuals.