The Maximally Efficient Generation Approach (MEGA) is a method to find approximate solutions in a region where strong differential rotation (ω-effect) and helicity (α-effect) coexist (Ruzmaikinet al., 1990). In this paper, new general MEGA-type solutions were obtained in the form of simple analytical formulas. It is shown that MEGA gives a WKBJ type solution to αω-dynamo problem with turning point at the maximum of the product of α- and ω-effects. MEGA attains a higher accuracy if there is a clear maximum of this product in real space far from the boundaries, which is the most usual case in real situations. The approximated eigenvalue depends crucially on the distribution of the product of α- and ω-effects, but not much on the particular distributions of the individual effects. The predicted eigenvalues and eigenfunctions were compared with the solutions from numerical analysis. It was found that the critical Reynolds numbers and oscillation frequencies predicted by the MEGA method are very close to the numerically obtained results for models with reasonable parameters. This gives strong support for MEGA estimations as simple and effective means for finding the region of parameters responsible for the astrophysical dynamos. However, the difference between the MEGA and numerical results become large when the maximum of generation is located near the outer boundary or when there is very small overlap of α- and ω-effects. For successful MEGA predictions, the difference between the MEGA and numerical critical Reynolds numbers (of dipole or quadrupole family, whichever is the smaller) is similar to the difference between the numerical solutions for the dipole and quadrupole modes.