We consider the compactification of M-theory on X7 with Betti numbers (b0, b1, b2, b3, b3, b2, b1, b0) and define a generalized mirror symmetry (b0, b1, b2, b3) → (b0, b1, b2 − ρ/2, b3 + ρ/2) under which ρ ≡ 7b0 − 5b1 + 3b2 − b3 changes sign. Generalized self-mirror theories with ρ = 0 have massless sectors with vanishing trace anomaly (before dualization). Examples include pure supergravity with {\mathcal N} \ge 4 and supergravity plus matter with {\mathcal N} \le 4.