In general, methods of hydroprocessing a hydrocarbonaceous feed stock are provided that do not use a costly recycle gas compressor, but are still able to use the more efficient reaction systems provided in a substantially three-phase hydroprocessing zone. The method combines a substantially liquid-phase hydroprocessing zone with the substantially three-phase hydroprocessing zone in a manner so that the hydrogen requirements for both reaction zones can be provided from an external source thereto without the use of a hydrogen recycle or recycle gas compressor to the substantially three-phase reaction zone.