Creating expressive character animations is labor-intensive, requiring intricate manual adjustment of animators across space and time. Previous works on controllable motion generation often rely on a predefined set of dense spatio-temporal specifications (e.g., dense pelvis trajectories with exact per-frame timing), limiting practicality for animators. To process high-level intent and intuitive control in diverse scenarios, we propose a practical controllable motions synthesis framework that respects sparse and flexible keyjoint signals. Our approach employs a decomposed diffusion-based motion synthesis framework that first synthesizes keyjoint movements from sparse input control signals and then synthesizes full-body motion based on the completed keyjoint trajectories. The low-dimensional keyjoint movements can easily adapt to various control signal types, such as end-effector position for diverse goal-driven motion synthesis, or incorporate functional constraints on a subset of keyjoints. Additionally, we introduce a time-agnostic control formulation, eliminating the need for frame-specific timing annotations and enhancing control flexibility. Then, the shared second stage can synthesize a natural whole-body motion that precisely satisfies the task requirement from dense keyjoint movements. We demonstrate the effectiveness of sparse and flexible keyjoint control through comprehensive experiments on diverse datasets and scenarios.