The clock-like diversification of Rice yellow mottle virus (RYMV), a widespread RNA plant virus that infects rice in Africa, was tested following a three-step approach with (i) an exhaustive search of recombinants, (ii) a comprehensive assessment of the selective constraints over lineages, and (iii) a stepwise series of tests of the molecular clock hypothesis. The first evidence of recombination in RYMV was found in East Africa, in the region most favorable to co-infection. RYMV evolved under a pronounced purifying selection, but the selection pressure did vary among lineages. There was no phylogenetic evidence of transient deleterious mutations. ORF2b, which codes for the polymerase and is the most constrained ORF, tends to diversify clock-like. With the other ORFs and the full genome, the departure from the strict clock model was limited. This likely reflects the dominant conservative selection pressure and the clock-like fixation of synonymous mutations.