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We currently have limited understanding of how complex data (e.g. algebraic data types) can be represented and manipulated in reversible machine code, in particular without generating garbage. In this paper we present methods for representing and manipulating binary trees (constructor terms) in the heap of a reversible machine. We also give methods for enforcing the so-called first-match policy for a simplified version of the recent reversible functional language RFUN by Yokoyama et al., and simple methods to support let-calls via stack environments.