Consistency models have recently been introduced to accelerate sampling from diffusion models by directly predicting the solution (i.e., data) of the probability flow ODE (PF ODE) from initial noise. However, the training of consistency models requires learning to map all intermediate points along PF ODE trajectories to their corresponding endpoints. This task is much more challenging than the ultimate objective of one-step generation, which only concerns the PF ODE's noise-to-data mapping. We empirically find that this training paradigm limits the one-step generation performance of consistency models. To address this issue, we generalize consistency training to the truncated time range, which allows the model to ignore denoising tasks at earlier time steps and focus its capacity on generation. We propose a new parameterization of the consistency function and a two-stage training procedure that prevents the truncated-time training from collapsing to a trivial solution. Experiments on CIFAR-10 and ImageNet $64\times64$ datasets show that our method achieves better one-step and two-step FIDs than the state-of-the-art consistency models such as iCT-deep, using more than 2$\times$ smaller networks. Project page: https://truncated-cm.github.io/