In this talk, we present two key contributions to the theory and practice of the AMLI-cycle multigrid method. First, we revisit the classical Chebyshev-accelerated AMLI-cycle. By establishing a new theory for its uniform convergence based solely on the two-grid convergence rate, we eliminate the costly requirement of estimating extreme eigenvalues on all coarse levels. This significantly simplifies implementation. Second, and more importantly, we introduce a novel momentum-accelerated AMLI-cycle. This new method uses polynomials derived from momentum acceleration techniques, ensuring a uniformly bounded condition number without needing anyeigenvalue or two-grid rate estimations. This makes its implementation as straightforward as standard V- or W-cycles. We prove that the quadratic momentum-accelerated AMLI-cycle is asymptotically optimal, matching the performance of its Chebyshev counterpart. Numerical results across various problems confirm the robustness and efficiency of our new approach, demonstrating performance on par with the Chebyshev-based method.