Within consumer research, ambiguity is often regarded as something to be avoided or eliminated. This article argues that ambiguity should be embraced, appreciated and understood as a multifaceted phenomenon found in manifold forms. An empirical study of one of the world's biggest brands, RMS Titanic, reveals that one of ambiguity's most characteristic forms, humour, is everywhere apparent. Titanic brand culture is comedic to the core, absurd though this seems on the surface. Three categories of ambiguous brand amusement are identified in the vast cultural complex surrounding Titanic and the oceanic implications for branding's received wisdom are considered. The article concludes with the contention that ambiguity strengthens rather than weakens unfathomable brands such as Titanic. Copyright © 2013 John Wiley & Sons, Ltd.