Multilevel converters have enabled various applications that are not possible with conventional two-level converters. Many of these applications, however, need a high output bandwidth, often approaching the switching or tolerated loss limit of the transistors, and still high quality, e.g., to actively stabilize and dampen a DC grid or specifically excite certain molecules or neural circuits in medical applications. Modulation in multilevel converters has two dimensions for improving the output quality, namely temporal switching modulation and amplitude quantization. A high bandwidth approaching the switching rate challenges existing modulation methods: carrier-based switching modulation is fine at low frequencies but experiences interaction between the carrier and the signal at the upper end of the spectrum; fundamental-frequency switching, such as nearest-level modulation (NLM), perform well at high frequencies but cause intolerable distortion for low frequency contents. We propose a hybrid modulation concept that can combine any methods from these two classes. It passes the error of a fundamental frequency method through a filtered switching modulator to combine the high output quality of the latter with the high bandwidth of the former. We optimize the filter to avoid under-modulation of the signal with the carrier of the modulator and to achieve the minimum overall distortion throughout a wide output bandwidth. We demonstrate the performance experimentally with a cascaded-bridge converter and compare it with the best prior arts. This technique ensures a usable output bandwidth up to 100% of the switching rate and maintains a total distortion level below 3%.Â