The correlation-consistent polarized valence basis sets (cc-pVXZ) for the atoms boron through neon have been extended to treat core and core-valence correlation effects. Basis functions were added to the existing cc-pVXZ sets to form correlation-consistent polarized core-valence sets (cc-pCVXZ) in the usual pattern : Double zeta added (1s1p), triple zeta added (2s2p1d), quadruple zeta added (3s3p2d1f), and quintuple zeta added (4s4p3d2f1g). The exponents of the core functions were determined by minimizing the difference between all-electron and valence-only correlation energies obtained from HF+1+2 calculations on the ground states of the atoms. With the cc-pCVXZ sets, core, core-valence, and valence correlation energies all converge exponentially toward apparent complete basis set (CBS) limits, as do the corresponding all-electron singles and doubles CI energies. Several test applications of the new sets are presented : The first two ionization potentials of boron, the P-3-S-5 separation in carbon, and the (X) over tilde(3)B(1)-(a) over tilde(1)A(1) state separation in CH2. As expected, correlation effects involving the core electrons of the first row atoms, B-Ne, are small but must be included if high accuracy is required.