We report results from a fast, efficient, and first-principles full-potential Nth-order muffin-tin orbital (FP-NMTO) method combined with van Leeuwen-Baerends correction to local density exchange-correlation potential. We show that more complete and compact basis set is critical in improving the electronic and structural properties. We exemplify the self-consistent FP-NMTO calculations on group IV and III-V semiconductors. Notably, predicted bandgaps, lattice constants, and bulk moduli are in good agreement with experiments (e.g. we find for Ge 0.86 eV, 5.57 [Formula: see text], 75 GPa versus measured 0.74 eV, 5.66 [Formula: see text], 77.2 GPa). We also showcase its application to the electronic properties of 2-dimensional h-BN and h-SiC, again finding good agreement with experiments.