Leakage currents through insulators have received continuous attention for several decades, owing to their importance in a wide range of technologies and interest in their fundamental mechanisms. This work investigates leakage currents through atomic layer deposited Al2O3 grown on SrTiO3. This combination is not only a key building block for oxide electronics but also a clean system for studying the leakage mechanisms without interfacial layers that form on most of the conventional bottom electrodes. We show how tiny differences in the deposition process can have a dramatic effect on the leakage behavior. A detailed analysis of the leakage behavior rules out Fowler-Nordheim tunneling (FNT) and thermionic emission. We conclude that the conduction mechanism is trap-related, and we ascribe it to trap-assisted tunneling or to Poole-Frenkel mechanisms. After annealing the sample in air, currents are reduced, which is ascribed to the transition from a trap-based mechanism to FNT, due to the elimination of the traps. The dramatic role of the assumptions regarding the flatband voltage used for analysis is critically discussed, and the sensitivity of the extracted parameters to this magnitude is quantitatively described. We show that future field-effect devices based on structures similar to those described here should be able to modulate >1013 electrons/cm2 in their channels. These results demonstrate ideas for reducing and analyzing leakage currents in insulators and highlight some of the possible approaches and pitfalls in their analysis, stressing the importance of the flatband voltage on the extracted parameters.