Degeneracy of the genetic code was attributed by Crick to imprecise hydrogen-bonded base-pairing at the wobble position during codon-anticodon pairing. The Crick wobble rules define but do not explain the RNA base pair combinations allowed at this position. We select six pyrimidine bases functioning as anticodon wobble bases (AWBs) to study their H-bonded pairing properties with the four major RNA bases using density functional theory at the B3LYP/6-31G(d,p) level. This is done to assess the extent to which the configuration of a solitary RNA wobble base pair may in itself determine specificity and degeneracy of the genetic code by allowing or disallowing the given base pair during codon-anticodon pairing. Calculated values of select configuration markers for the base pairs screen well between allowed and disallowed base pairs for most cases examined here, where the base pair width emerges as an important factor. A few allowed wobble pairs invoke the involvement of RNA nucleoside conformation, as well as involvement of the exocyclic substituent in H-bonding. This study, however, cannot explain the disallowed status of the Ura⋯Gua wobble pair on the basis of configuration alone. Explanation of the allowed status of the V⋯Ura pair requires further study on the mediatory role of water molecules. Apart from these two cases, these computational results are sufficient, on the basis of base pair configuration alone, to account for the specificity and degeneracy of the genetic code for all known cases of codon-anticodon pairing which involve the pyrimidine AWBs studied here.