To design successful new products and services, managers need to measure consumer preferences relative to product attributes. Many existing methods use ordinal measures. Intensity measures have the potential to provide more information per question, thus allowing more accurate models or fewer consumer questions (lower survey cost, less consumer wearout). To exploit this potential, researchers must be able to identify how consumers react to these questions and must be able to estimate intensity-based preference functions. This paper provides a general structure for using intensity measures for estimating consumer preference functions. Within the structure: (1) alternative measurement theories are reviewed, (2) axioms for developing testable implications of each theory are provided, (3) statistical tests to test these implications and distinguish which theory describes how consumers are using the intensity measures are developed, (4) functional forms appropriate for the preference functions implied by each theory are derived, and (5) procedures to estimate the parameters of these preference functions are provided. Based on these results, a practical procedure, implemented by an interactive computer package, to measure preference functions in a market research environment is developed. An empirical case illustrates how the statistical tests and estimation procedures are used to aid in the design of new telecommunications devices. Empirical results suggest the majority of consumers can provide intensity judgments. The intensity-based estimation procedures do better on several criteria than ordinal estimation.