A communication protocol based on a Gaussian modulation of squeezed states in a single quadrature and measured via homodyne detection can completely eliminate information leakage to an eavesdropper in a pureloss channel. However, the asymmetry of the protocol with respect to the quadratures of light presents security issues and the eavesdropper’s information is not necessarily minimized for general asymmetric attacks. Here, we perform asymptotic security analysis of the asymmetric protocol against general asymmetric collective attacks and bound the eavesdropper’s information via the Heisenberg uncertainty principle. The bound is not tight, and therefore we symmetrize the protocol in a heralding way, discarding the issues of asymmetry altogether. Our proposed heralding protocol asymptotically eliminates information leakage in a pure-loss channel and minimizes leakage in a noisy channel.