The National Institute of Radiological Sciences (NIRS) has extensively studied carbon-ion radiotherapy at the Heavy-Ion Medical Accelerator in Chiba (HIMAC) with some positive outcomes, and has established its efficacy. Therefore, efforts to distribute the therapy to the general public should be made, for which it is essential to enable direct application of clinical and technological experiences obtained at NIRS. For widespread use, it is very important to reduce the cost through facility downsizing with minimal acceleration energy to deliver the HIMAC-equivalent clinical beams. For the beam delivery system, the requirement of miniaturization is translated to reduction in length while maintaining the clinically available field size and penetration range for range-modulated uniform broad beams of regular fields that are either circular or square for simplicity. In this paper, we evaluate the various wobbling methods including original improvements, especially for application to the compact facilities through the experimental and computational studies. The single-ring wobbling method used at HIMAC is the best one including a lot of experience at HIMAC but the residual range is a fatal problem in the case of a compact facility. On the other hand, uniform wobbling methods such as the spiral and zigzag wobbling methods are effective and suitable for a compact facility. Furthermore, these methods can be applied for treatment with passive range modulation including respiratory gated irradiation. In theory, the choice between the spiral and zigzag wobbling methods depends on the shape of the required irradiation field. However, we found that it is better to use the zigzag wobbling method with transformation of the wobbling pattern even when a circular uniform irradiation field is required, because it is difficult to maintain the stability of the wobbler magnet due to the rapid change of the wobbler current in the spiral wobbling method. The regulated wobbling method, which is our improvement, can well expand the uniform irradiation field and lead to reducing the power requirement of the wobbler magnets. Our evaluations showed that the regulated zigzag wobbling method is the most suitable method for use in currently designed compact carbon-therapy facilities.