Following a previous study on the effects of manipulating cognitive complexity on the oral production of a monologic information-giving task (Santos 2018), this quantitative research work aims to investigate the impact of increasing the cognitive demands of an argumentative task. The independent variable chosen was the “± few elements” of the Cognition Hypothesis proposed by Robinson (2001, 2003, 2005, 2010, 2011, 2015). The dependent variables were measures of accuracy and measures of linguistic complexity (syntactic complexity and lexical diversity). For accuracy, two general measures (error-free clauses per total clauses and errors per 100 words) and four specific measures (lexical errors per AS-unit, omissions per AS-unit, morphosyntactic errors per AS-unit and the percentage of self-repairs per total errors) were selected. As syntactic complexity measures, clause length (words per clause) was calculated as well as subordination (clauses per AS-unit) and coordination (coordination clauses per AS-unit). Lexical diversity was measured by Guiraud’s index. Thirty-three Chinese learners of Portuguese as a foreign language participated in the study. They performed two argumentative oral tasks (simple and complex task). The order of the tasks was counterbalanced. All data were transcribed and coded in the CLAN program (MacWhinney, 2000). The findings showed that increasing task complexity led to a more lexically diverse speech. The Cognition Hypothesis was confirmed only concerning lexical diversity. A correlational analysis between accuracy and complexity measures did not confirm trade-off effects, as predicted by the Limited Attentional Capacity approach (Skehan 1998, 2009, 2014, 2015, 2018). The findings of this work are compared with the findings of a previous study with a different task type, i.e., an information-giving task (Santos 2018). As both studies analyse L2 oral performance in Portuguese, the discussion of the results can bring new insights to the area of Applied Linguistics, namely to the field of Instructed Second Language Acquisition.