We extend the cascade-exciton model (CEM), and the Los Alamos version of the quark-gluon string model (LAQGSM), event generators of the Monte Carlo N-particle transport code version 6 (MCNP6), to describe production of energetic light fragments (LF) heavier than He4 from various nuclear reactions induced by particles and nuclei at energies up to about 1 TeV/nucleon. In these models, energetic LF can be produced via Fermi breakup, preequilibrium emission, and coalescence of cascade particles. Initially, we study several variations of the Fermi breakup model and choose the best option for these models. Then, we extend the modified exciton model (MEM) used by these codes to account for a possibility of multiple emission of up to 66 types of particles and LF (up to Mg28) at the preequilibrium stage of reactions. Then, we expand the coalescence model to allow coalescence of LF from nucleons emitted at the intranuclear cascade stage of reactions and from lighter clusters, up to fragments with mass numbers A≤7, in the case of CEM, and A≤12, in the case of LAQGSM. Next, we modify MCNP6 to allow calculating and outputting spectra of LF and heavier products with arbitrary mass and charge numbers. The improved version of CEM is implemented into MCNP6. Finally, we test the improved versions of CEM, LAQGSM, and MCNP6 on a variety of measured nuclear reactions. The modified codes give an improved description of energetic LF from particle- and nucleus-induced reactions; showing a good agreement with a variety of available experimental data. They have an improved predictive power compared to the previous versions and can be used as reliable tools in simulating applications involving such types of reactions.