The performance of gradient methods has been considerably improved by the introduction of delayed parameters. Recently, the revealing of second-order information has given rise to the Cauchy-based methods with alignment, which are generally considered as the state of the art of gradient methods. This paper investigates the spectral properties of minimal gradient and asymptotically optimal steps, and then suggests three fast methods with alignment without using the Cauchy step. The convergence results are provided, and numerical experiments show that the new methods provide competitive alternatives to the classical Cauchy-based methods. In particular, alignment gradient methods present advantages over the Krylov subspace methods in some situations, which makes them attractive in practice.