We present a concise yet effective central-moments-based lattice Boltzmann method with an accelerated convergence to the steady state through preconditioning. It is demonstrated that the proposed scheme reduces to a slight modification of the unaccelerated one, as the preconditioning affects only the equilibrium state. Different from previous efforts carried out within the lattice Boltzmann community, the present scheme is built on an original model. In fact, the corresponding collision operator loses the pyramidal orchestrated nature that is typical of the cascaded scheme, hence we coin the name "noncascaded." Our model is very general, characterized by highly intelligible formulations, simple to implement, and it can be derived for any lattice velocity space.