Virus genomes may encode overlapping or nested open reading frames that increase their coding capacity. It is not known whether the constraints on spatial structures of the two encoded proteins limit evolvability of nested genes. We examine the evolution of a pair of proteins, p22 and p19, encoded by nested genes in plant viruses from the genus Tombusvirus. The known structure of p19, a suppressor of RNA silencing, belongs to the RAGNYA fold from the alpha+beta class. The structure of p22, the cell-to-cell movement protein from the 30K family widespread in plant viruses, is predicted with the AlphaFold approach, suggesting a single jelly-roll fold core from the all-beta class, structurally similar to capsid proteins from plant and animal viruses. The nucleotide and codon preferences impose modest constraints on the types of secondary structures encoded in the alternative reading frames, nonetheless allowing for compact, well-ordered folds from different structural classes in two similarly-sized nested proteins. Tombusvirus p22 emerged through radiation of the widespread 30K family, which evolved by duplication of a virus capsid protein early in the evolution of plant viruses, whereas lineage-specific p19 may have emerged by stepwise increase in the length of the overprinted gene and incremental acquisition of functionally active secondary structure elements by the protein product. This evolution of p19 towards the RAGNYA fold represents one of the first documented examples of protein structure convergence in naturally occurring proteins.