We describe our attempts to improve upon the quality of the KT1 and KT2 generalized gradient approximation (GGA) exchange-correlation functionals [T. W. Keal and D. J. Tozer, J. Chem. Phys. 119, 3015 (2003)], through the introduction of additional gradient-corrected exchange and correlation terms. A GGA functional, denoted KT3, is presented, which maintains the high quality main-group nuclear magnetic resonance shielding constants obtained with KT1 and KT2; results are 2-3 times more accurate than conventional GGA and hybrid functionals. For the extensive range of systems considered in this study, KT3 also provides atomization energies, ionization potentials, electron affinities, proton affinities, bond angles, and electronic polarizabilities that are comparable to, or that surpass, those of the best present-day GGAs. Furthermore, it provides equilibrium molecular bond lengths and diatomic harmonic vibrational wave numbers that are as accurate as those from the best hybrid functionals. Further improvements are required in the description of classical chemical reaction barriers.