We investigate the effects of smoothness of basis functions on solution accuracy within the isogeometric analysis framework. We consider two simple one-dimensional structural eigenvalue problems and two static shell boundary value problems modeled with trivariate NURBS solids. We also develop a local refinement strategy that we utilize in one of the shell analyses. We find that increased smoothness, that is, the “ k-method,” leads to a significant increase in accuracy for the problems of structural vibrations over the classical C 0 -continuous “ p-method,” whereas a judicious insertion of C 0 -continuous surfaces about singularities in a mesh otherwise generated by the k-method, usually outperforms a mesh in which all basis functions attain their maximum level of smoothness. We conclude that the potential for the k-method is high, but smoothness is an issue that is not well understood due to the historical dominance of C 0 -continuous finite elements and therefore further studies are warranted.