We investigate how increasing the complexity of the message space, in the presence of limited memory, can reduce misrepresentation in strategic communication. We enrich a standard cheap talk game so that senders must communicate not just a payoff-relevant state, but also payoff-irrelevant attributes correlated with the state. We show that: i) increasing the set of attributes that may need to be reported (i.e., the complexity of the game) improves the amount of information transmitted in equilibrium, ii) too much of an increase in complexity leads to a reversal of those gains, iii) limited memory on the part of players, as well as the relative complexity faced by senders and receivers, drives these changes, and iv) individuals experience cognitive costs when dealing with complex environments that they are willing to pay to avoid. Our findings demonstrate that the reporting of redundant information may induce equilibria that feature improved outcomes compared to simpler, more direct reporting systems, and point out the importance of complexity when trying to induce truthful information revelation.