This paper proposes a low-complexity coding strategy for the flat fading Gaussian Multiple Access Channel (MAC) based on the concept of Compute-and-Forward. To assess the performance of the proposed coding scheme, we compare the block error probability of a particular code implementation with that of an optimal Gaussian MAC code with the same rates, when applied to our slow fading Gaussian MAC. We show by simulation that even using very short codewords, our strategy beats standard Successive Interference Cancellation techniques by obtaining a good performance with low coding and decoding complexity.