  We introduce $\mathsf{LAM}$, a subsystem of $\mathsf{IMALL}_2$ with
restricted additive rules able to manage duplication linearly, called
\textit{linear additive rules}. $\mathsf{LAM}$ is presented as the type
assignment system for a calculus endowed with copy constructors, which deal
with substitution in a linear fashion. As opposed to the standard additive
rules, the linear additive rules do not affect the complexity of term
reduction: typable terms of $\mathsf{LAM}$ enjoy linear strong normalization.
Moreover, a mildly weakened version of cut-elimination for this system is
proven which takes a cubic number of steps. Finally, we define a sound
translation from $\mathsf{LAM}$'s proofs into $\mathsf{IMLL}_2$'s linear lambda
terms, and we study its complexity.
