Whether consecutive interpreting (CI) should be taught systematically in all interpreter training programs is a frequently debated question. One argument made forcefully against including CI training is that consecutive is gradually disappearing from the market. This claim is made mostly in Western Europe; in other markets, and in particular in Asia and in Eastern Europe, consecutive seems to be as lively as ever, due to its distinct advantages over simultaneous (less costly, less cumbersome in terms of equipment, more flexible overtime and space). A further argument made against CI training is that in programs serving a market where this mode of interpretation is not required, learning consecutive means devoting much time and energy to the acquisition of skills not relevant to the market, time and energy that would be better invested in simultaneous. Some, however, counter this argument by claiming that simultaneous is just an 'accelerated consecutive' and that the skills of consecutive are therefore relevant to simultaneous. This paper looks more closely at the nature of consecutive in cognitive terms, and brings this analysis into the debate.