Random lasers hold the premise for cheap coherent light sources that can be miniaturized and molded into any shape and used for speckle-free imaging in biology, remote sensing, display technology, encrypting, cancer detection and distributed amplification. However, they require improvements specifically in terms of efficiency and low emission threshold. This work details for the first time a strategy for increasing the efficiency of a random laser that consists in using smaller particles, trapped between large particles to serve as absorption and gain centers whereas the large particles control mainly the light diffusion into the sample. A record slope efficiency of more than 50% was achieved using yttrium vanadate particles with mean particle size of 54 ??m by optimizing the distribution of the polydispersed particles. In addition, random lasing with very low emission threshold (0.24 mJ/cm2) is also reported in a strongly disordered optical medium that is in the transition regime to Anderson localization composed by a colloidal suspension of core???shell TiO2@ Silica nanoparticles in ethanol solution of rhodamine 6G. A promising method called fraction of absorbed pump power allowed us to infer the emission threshold for localized modes (peaks mode). The classical super-fluorescence band (ASE) of the random laser was measured separately by collecting the emission at the back of the samples, showing a linear dependence with pumping fluence without gain depletion. The intensity of peaks during Anderson transition is approximately equal within a broad frequency range, indicating suppression of the interaction between the peak modes. The random lasers have been characterized by measurements of backscattering cone, absorption and reflection measurement, transport mean free path, average photon path length and fill fractions.