$p-Clique ≤fpt p-MC(Σ_1)$. $(G, k) ↦ (G, clique_k)$ with $clique_k = ∃x_0 … ∃x_{k-1} ⋀_{i<j<k} (¬ x_i = x_j ∧ E x_i x_j)$ (the conjunction closed by $x_0 = x_0$), for $1 ≤ k ≤ n$; $k = 0$ goes to a fixed yes-instance and $k > n$ to a fixed no-instance. The new parameter is at most $10 (k + 1)²$, and the map is computed by an IMP+ program in $O(|x|³)$ steps.