This paper proposes two ways to fix the broken Square-Vinegar signature scheme. We give heuristic arguments as well as experimental evidence to support the security claims. The first variant, Square-Vinegar with Embedding, uses a simple modification that nonetheless changes the nature of the public key polynomials. The second, 2-Square-Vinegar, is a more significant overhaul of the construction, using a bivariate secret map instead of a univariate one.