Much comparative research aimed at establishing differences in intelligence among vertebrates has failed to convince the sceptic, because it has concentrated on a single experimental paradigm (such as learning sets), while employing a diverse array of species in the hope of establishing a rank ordering of intelligence. The sceptic can insist that such research has not even established that there are any differences in mechanisms of intelligence between any pair of vertebrate species, let alone elucidated the nature of the difference, and even the unsceptical will doubt that such research is ever likely to establish a rank order of intelligence. It is more informative to concentrate on fewer species, but a broader range of experimental paradigms. Thus, studies of serial reversal learning have consistently suggested that goldfish do not show such rapid improvement as do rats. One explanation of this might be that rats learn more effectively than goldfish to use the outcome of one trial to predict the outcome of the next. The suggestion is supported by finding other experimental paradigms, such as alternation learning, which must also tap such a process, and where rats again learn more rapidly than goldfish. Efficient learning-set performance may also depend on this process, but must in addition require the subject to transfer this rule across changes of stimuli. There is reason to believe that not all vertebrates are equally adept at such transfer, and this possibility is explored in a series of experiments studying the transfer of matching-to-sample in pigeons and corvids. The corvids display significantly better transfer and the close similarity in training procedures possible with these subjects makes it unlikely that this is due to differences in these training procedures.