Conservation is often used to define essential sequences within RNA sites. However, conservation finds only invariant sequence elements that are necessary for function, rather than finding a set of sequence elements sufficient for function. Biochemical studies in several systems-including the hammerhead ribozyme and the purine riboswitch-find additional elements, such as loop-loop interactions, required for function yet not phylogenetically conserved. Here we define a critical test of sufficiency: We embed a minimal, apparently sufficient motif for binding the amino acid tryptophan in a random-sequence background and ask whether we obtain functional molecules. After a negative result, we use a combination of three-dimensional structural modeling, selection, designed mutations, high-throughput sequencing, and bioinformatics to explore functional insufficiency. This reveals an essential unpaired G in a diverse structural context, varied sequence, and flexible distance from the invariant internal loop binding site identified previously. Addition of the new element yields a sufficient binding site by the insertion criterion, binding tryptophan in 22 out of 23 tries. Random insertion testing for site sufficiency seems likely to be broadly revealing.