Construction Grammar has reached a stage of maturity where many researchers are looking for an explicit formal grounding of their work. Recently, there have been exciting developments to cater for this demand, most notably in Sign-Based Construction Grammar (SBCG) and Fluid Construction Grammar (FCG). Unfortunately, like playing a music instrument, the formalisms used by SBCG and FCG take time and effort to master, and linguists who are unfamiliar with them may not always appreciate the far-reaching theoretical consequences of adopting this or that approach. This paper undresses SBCG and FCG to their bare essentials, and offers a linguist-friendly comparison that looks at how both approaches define constructions, linguistic knowledge and language processing.