This paper explores the interaction of regularity and idiosyncracy in the formation of nominals. It treats both nominals whose formation is highly regular, such as red box, and nominals whose formation is rather idiosyncratic, such as the Big Mess Construction (bmc; so good a bargain) and the Binominal Noun Phrase Construction (bnpc; her nitwit of a husband). Both the bmc and the bnpc conform to productive patterns, but the proper place of those patterns in the grammar as a whole is not easy to identify. To rise to the challenge, we build on recent developments in Head-driven Phrase Structure Grammar and the more formally inclined strands of Construction Grammar. Taking a cue from the treatment of clausal constructions in Ginzburg & Sag (2000), we develop a bi-dimensional hierarchy of nominal phrase types, in which the regular nominals inherit their properties from independently motivated higher types, while the idiosyncratic nominals are characterized by a mixture of inherited and inherent properties. The resulting treatment is sufficiently flexible to deal with the subtle interaction between the regular and the idiosyncratic, and sufficiently rigorous to be falsifiable. It is also compared with alternative treatments.