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We show that the secrecy function conjecture that states that the maximum ofthe secrecy function of an $l$-modular lattice occurs at $1/\sqrt{l}$ is false,by proving that the 4-modular lattice $C^(4) = \mathbb{Z} \oplus\sqrt{2}\mathbb{Z} \oplus 2\mathbb{Z}$ fails to satisfy this conjecture. Wealso indicate how the secrecy function must be modified in the $l$-modular caseto have a more reasonable chance for it to have a maximum at $1/\sqrt{l}$, andshow that the conjecture, modified with this new secrecy function, is true forvarious odd 2-modular lattices.

Counterexample to the $l$-modular Belfiore-Sol\'e Conjecture