An alternative-transforms-based scheme has recently been proposed to achieve perceptual encryption of video signals in which multiple transforms are designed by using different rotation angles at the final stage of the discrete cosine transforms (DCTs) butterfly flow-graph structure. More recently, it is found that a set of more efficient alternative transforms can be derived by introducing sign-flips at the same stage, which is equivalent to an extra rotation angle of π. In this paper, we generalize this sign-flipping technique by randomly embedding sign-flips into all stages of the DCTs butterfly structure so that the encryption space becomes much larger to yield a higher security. We pursue this study for H.264-compatible videos, assuming that the integer DCT of size 4 × 4 is used. First, we follow the separable implementation of the 4 × 4 2-D DCT in which different sign-flipping strategies will be employed along its horizontal and vertical dimensions. Second, we convert the 4 × 4 2-D DCT into a 16-point 1-D butterfly structure so that more sign-flips can be embedded at its various stages. Third, we choose different schemes to pair the node-variables in the 16-point 1-D butterfly structure, thus further enlarging the encryption space. Extensive experiments are conducted to show the performance of these improved encryption schemes and some security analyzes are also presented to confirm their persistence to various attacking strategies.