Productivity of argument structure constructions is a new emerging field within cognitive-functional linguistics. The term productivity as used in linguistic research contains at least three subconcepts: 'extensibility', 'regularity', and 'generality'. The focus in this study of case and argument structure constructions in Icelandic is on the concept of extensibility, while generality and regularity are regarded as derivative of extensibility. Productivity is considered to be a function of type frequency, semantic coherence, and the inverse correlation between these two. This study establishes productivity as an emergent feature of the grammatical system, in an analysis that is grounded in a usage-based constructional approach, where constructions are organized into lexicality-schematicity hierarchies. The view of syntactic productivity advocated here offers a unified account of productivity, in that it captures different degrees of productivity, ranging from highly productive patterns through various intermediate degrees of productivity to low-level analogical extensions.