We consider the Gaussian interference channel with an intermediate relay. The known achievable schemes for this channel are based on decode-and-forward (DF) relaying, whose performance depends on the signal-to-noise (SNR) ratio of the received signal at the relay. Consequently, when the source-torelay (S - R) links are weak, the resulting achievable rates have room for improvement. In this work, we design achievable schemes that provide this improvement. First, we consider compress-and-forward (CF) relaying to overcome the weakness of the DF schemes. Second, we consider employing structured codes and observe that when the signal strength from the direct link is subject to severe attenuation, using nested lattice codes yields higher rates than both the DF and CF schemes. Numerical results are presented to demonstrate the performance of different achievable schemes with the Potent Relay Outerbound derived in our previous work.