Many attempts have been made to correlate degrees of both animal and human intelligence with brain properties. With respect to mammals, a much-discussed trait concerns absolute and relative brain size, either uncorrected or corrected for body size. However, the correlation of both with degrees of intelligence yields large inconsistencies, because although they are regarded as the most intelligent mammals, monkeys and apes, including humans, have neither the absolutely nor the relatively largest brains. The best fit between brain traits and degrees of intelligence among mammals is reached by a combination of the number of cortical neurons, neuron packing density, interneuronal distance and axonal conduction velocity--factors that determine general information processing capacity (IPC), as reflected by general intelligence. The highest IPC is found in humans, followed by the great apes, Old World and New World monkeys. The IPC of cetaceans and elephants is much lower because of a thin cortex, low neuron packing density and low axonal conduction velocity. By contrast, corvid and psittacid birds have very small and densely packed pallial neurons and relatively many neurons, which, despite very small brain volumes, might explain their high intelligence. The evolution of a syntactical and grammatical language in humans most probably has served as an additional intelligence amplifier, which may have happened in songbirds and psittacids in a convergent manner.